Advertisement
| algebraic structures and their applications: Algebraic Structures and Applications Sergei Silvestrov, Anatoliy Malyarenko, Milica Rančić, 2020-06-18 This book explores the latest advances in algebraic structures and applications, and focuses on mathematical concepts, methods, structures, problems, algorithms and computational methods important in the natural sciences, engineering and modern technologies. In particular, it features mathematical methods and models of non-commutative and non-associative algebras, hom-algebra structures, generalizations of differential calculus, quantum deformations of algebras, Lie algebras and their generalizations, semi-groups and groups, constructive algebra, matrix analysis and its interplay with topology, knot theory, dynamical systems, functional analysis, stochastic processes, perturbation analysis of Markov chains, and applications in network analysis, financial mathematics and engineering mathematics. The book addresses both theory and applications, which are illustrated with a wealth of ideas, proofs and examples to help readers understand the material and develop new mathematical methods and concepts of their own. The high-quality chapters share a wealth of new methods and results, review cutting-edge research and discuss open problems and directions for future research. Taken together, they offer a source of inspiration for a broad range of researchers and research students whose work involves algebraic structures and their applications, probability theory and mathematical statistics, applied mathematics, engineering mathematics and related areas. |
| algebraic structures and their applications: Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures Jana, Chiranjibe, Senapati, Tapan, Pal, Madhumangal, 2019-10-25 In the world of mathematics, the study of fuzzy relations and its theories are well-documented and a staple in the area of calculative methods. What many researchers and scientists overlook is how fuzzy theory can be applied to industries outside of arithmetic. The framework of fuzzy logic is much broader than professionals realize. There is a lack of research on the full potential this theoretical model can reach. The Handbook of Research on Emerging Applications of Fuzzy Algebraic Structures provides emerging research exploring the theoretical and practical aspects of fuzzy set theory and its real-life applications within the fields of engineering and science. Featuring coverage on a broad range of topics such as complex systems, topological spaces, and linear transformations, this book is ideally designed for academicians, professionals, and students seeking current research on innovations in fuzzy logic in algebra and other matrices. |
| algebraic structures and their applications: Neutrosophic Algebraic Structures and Their Applications Florentin Smarandache, Memet Şahin, Derya Bakbak, Vakkas Uluçay, Abdullah Kargın , 2022-08-01 Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more. |
| algebraic structures and their applications: Algebraic structures and their applications , 2002 |
| algebraic structures and their applications: An Introduction to Algebraic Structures Joseph Landin, 2012-08-29 This self-contained text covers sets and numbers, elements of set theory, real numbers, the theory of groups, group isomorphism and homomorphism, theory of rings, and polynomial rings. 1969 edition. |
| algebraic structures and their applications: Formal Moduli of Algebraic Structures O. A. Laudal, 2006-11-15 |
| algebraic structures and their applications: A Book of Abstract Algebra Charles C Pinter, 2010-01-14 Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition. |
| algebraic structures and their applications: Abstract Algebra David R. Finston, Patrick J. Morandi, 2014-08-29 This text seeks to generate interest in abstract algebra by introducing each new structure and topic via a real-world application. The down-to-earth presentation is accessible to a readership with no prior knowledge of abstract algebra. Students are led to algebraic concepts and questions in a natural way through their everyday experiences. Applications include: Identification numbers and modular arithmetic (linear) error-correcting codes, including cyclic codes ruler and compass constructions cryptography symmetry of patterns in the real plane Abstract Algebra: Structure and Application is suitable as a text for a first course on abstract algebra whose main purpose is to generate interest in the subject or as a supplementary text for more advanced courses. The material paves the way to subsequent courses that further develop the theory of abstract algebra and will appeal to students of mathematics, mathematics education, computer science, and engineering interested in applications of algebraic concepts. |
| algebraic structures and their applications: Discrete Groups, Expanding Graphs and Invariant Measures Alex Lubotzky, 1994-08-01 In the last ?fteen years two seemingly unrelated problems, one in computer science and the other in measure theory, were solved by amazingly similar techniques from representation theory and from analytic number theory. One problem is the - plicit construction of expanding graphs («expanders»). These are highly connected sparse graphs whose existence can be easily demonstrated but whose explicit c- struction turns out to be a dif?cult task. Since expanders serve as basic building blocks for various distributed networks, an explicit construction is highly des- able. The other problem is one posed by Ruziewicz about seventy years ago and studied by Banach [Ba]. It asks whether the Lebesgue measure is the only ?nitely additive measure of total measure one, de?ned on the Lebesgue subsets of the n-dimensional sphere and invariant under all rotations. The two problems seem, at ?rst glance, totally unrelated. It is therefore so- what surprising that both problems were solved using similar methods: initially, Kazhdan’s property (T) from representation theory of semi-simple Lie groups was applied in both cases to achieve partial results, and later on, both problems were solved using the (proved) Ramanujan conjecture from the theory of automorphic forms. The fact that representation theory and automorphic forms have anything to do with these problems is a surprise and a hint as well that the two questions are strongly related. |
| algebraic structures and their applications: Algebraic Structures and Their Representations José Antonio de la Peña, Ernesto Vallejo, Natig M. Atakishiyev, 2005 The Latin-American conference on algebra, the XV Coloquio Latinoamericano de Algebra (Cocoyoc, Mexico), consisted of plenary sessions of general interest and special sessions on algebraic combinatorics, associative rings, cohomology of rings and algebras, commutative algebra, group representations, Hopf algebras, number theory, quantum groups, and representation theory of algebras. This proceedings volume contains original research papers related to talks at the colloquium. In addition, there are several surveys presenting important topics to a broad mathematical audience. There are also two invited papers by Raymundo Bautista and Roberto Martinez, founders of the Mexican school of representation theory of algebras. The book is suitable for graduate students and researchers interested in algebra. |
| algebraic structures and their applications: A Physicists Introduction to Algebraic Structures Palash B. Pal, 2019-05-23 Algebraic structures including vector space, groups, topological spaces and more, all covered in one volume, showing the mutual connections. |
| algebraic structures and their applications: Abstract Algebra Celine Carstensen-Opitz, Benjamin Fine, Anja Moldenhauer, Gerhard Rosenberger, 2019-09-02 A new approach to conveying abstract algebra, the area that studies algebraic structures, such as groups, rings, fields, modules, vector spaces, and algebras, that is essential to various scientific disciplines such as particle physics and cryptology. It provides a well written account of the theoretical foundations and it also includes a chapter on cryptography. End of chapter problems help readers with accessing the subjects. |
| algebraic structures and their applications: Algebraic Structures George R. Kempf, 2012-12-06 The laws of composition include addition and multiplication of numbers or func tions. These are the basic operations of algebra. One can generalize these operations to groups where there is just one law. The theory of this book was started in 1800 by Gauss, when he solved the 2000 year-old Greek problem about constructing regular n-gons by ruler and compass. The theory was further developed by Abel and Galois. After years of development the theory was put in the present form by E. Noether and E. Artin in 1930. At that time it was called modern algebra and concentrated on the abstract exposition of the theory. Nowadays there are too many examples to go into their details. I think the student should study the proofs of the theorems and not spend time looking for solutions to tricky exercises. The exercises are designed to clarify the theory. In algebra there are four basic structures; groups, rings, fields and modules. We present the theory of these basic structures. Hopefully this will give a good introduc tion to modern algebra. I have assumed as background that the reader has learned linear algebra over the real numbers but this is not necessary. |
| algebraic structures and their applications: Combinatorial Structures in Algebra and Geometry Dumitru I. Stamate, Tomasz Szemberg, 2020-09-01 This proceedings volume presents selected, peer-reviewed contributions from the 26th National School on Algebra, which was held in Constanța, Romania, on August 26-September 1, 2018. The works cover three fields of mathematics: algebra, geometry and discrete mathematics, discussing the latest developments in the theory of monomial ideals, algebras of graphs and local positivity of line bundles. Whereas interactions between algebra and geometry go back at least to Hilbert, the ties to combinatorics are much more recent and are subject of immense interest at the forefront of contemporary mathematics research. Transplanting methods between different branches of mathematics has proved very fruitful in the past – for example, the application of fixed point theorems in topology to solving nonlinear differential equations in analysis. Similarly, combinatorial structures, e.g., Newton-Okounkov bodies, have led to significant advances in our understanding of the asymptotic properties of line bundles in geometry and multiplier ideals in algebra. This book is intended for advanced graduate students, young scientists and established researchers with an interest in the overlaps between different fields of mathematics. A volume for the 24th edition of this conference was previously published with Springer under the title Multigraded Algebra and Applications (ISBN 978-3-319-90493-1). |
| algebraic structures and their applications: Sets, Groups, and Mappings: An Introduction to Abstract Mathematics Andrew D. Hwang, 2019-09-26 This book introduces students to the world of advanced mathematics using algebraic structures as a unifying theme. Having no prerequisites beyond precalculus and an interest in abstract reasoning, the book is suitable for students of math education, computer science or physics who are looking for an easy-going entry into discrete mathematics, induction and recursion, groups and symmetry, and plane geometry. In its presentation, the book takes special care to forge linguistic and conceptual links between formal precision and underlying intuition, tending toward the concrete, but continually aiming to extend students' comfort with abstraction, experimentation, and non-trivial computation. The main part of the book can be used as the basis for a transition-to-proofs course that balances theory with examples, logical care with intuitive plausibility, and has sufficient informality to be accessible to students with disparate backgrounds. For students and instructors who wish to go further, the book also explores the Sylow theorems, classification of finitely-generated Abelian groups, and discrete groups of Euclidean plane transformations. |
| algebraic structures and their applications: Algebra without Borders – Classical and Constructive Nonassociative Algebraic Structures Mahouton Norbert Hounkonnou, Melanija Mitrović, Mujahid Abbas, Madad Khan, 2023-12-01 This book gathers invited, peer-reviewed works presented at the 2021 edition of the Classical and Constructive Nonassociative Algebraic Structures: Foundations and Applications—CaCNAS: FA 2021, virtually held from June 30 to July 2, 2021, in dedication to the memory of Professor Nebojša Stevanović (1962-2009). The papers cover new trends in the field, focusing on the growing development of applications in other disciplines. These aspects interplay in the same cadence, promoting interactions between theory and applications, and between nonassociative algebraic structures and various fields in pure and applied mathematics. In this volume, the reader will find novel studies on topics such as left almost algebras, logical algebras, groupoids and their generalizations, algebraic geometry and its relations with quiver algebras, enumerative combinatorics, representation theory, fuzzy logic and foundation theory, fuzzy algebraic structures, group amalgams, computer-aided development and transformation of the theory of nonassociative algebraic structures, and applications within natural sciences and engineering. Researchers and graduate students in algebraic structures and their applications can hugely benefit from this book, which can also interest any researcher exploring multi-disciplinarity and complexity in the scientific realm. |
| algebraic structures and their applications: Algebras, Graphs and their Applications Ilwoo Cho, 2013-09-11 This book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory connected with discrete and combinatorial mathematic |
| algebraic structures and their applications: Essentials of Abstract Algebra Sachin Nambeesan, 2025-02-20 Essentials of Abstract Algebra offers a deep exploration into the fundamental structures of algebraic systems. Authored by esteemed mathematicians, this comprehensive guide covers groups, rings, fields, and vector spaces, unraveling their intricate properties and interconnections. We introduce groups, exploring their diverse types, from finite to infinite and abelian to non-abelian, with concrete examples and rigorous proofs. Moving beyond groups, we delve into rings, explaining concepts like ideals, homomorphisms, and quotient rings. The text highlights the relevance of ring theory in number theory, algebraic geometry, and coding theory. We also navigate fields, discussing field extensions, Galois theory, and algebraic closures, and exploring connections between fields and polynomial equations. Additionally, we venture into vector spaces, examining subspaces, bases, dimension, and linear transformations. Throughout the book, we emphasize a rigorous mathematical foundation and intuitive understanding. Concrete examples, diagrams, and exercises enrich the learning experience, making abstract algebra accessible to students, mathematicians, and researchers. Essentials of Abstract Algebra is a timeless resource for mastering the beauty and power of algebraic structures. |
| algebraic structures and their applications: The Theory of Classes of Groups Guo Wenbin, 2012-12-06 One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of alge bras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. ln his re ports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Con ference and to another international mathematics congress, striking the ories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F. |
| algebraic structures and their applications: Categorical Structures and Their Applications Werner Ghler, Gerhard Preuss, Horst Herrlich, 2004 The book collects original research papers on applied categorical structures, most of which have been presented at the North-West European Category Seminar 2003 in Berlin. The spectrum of these mathematical results reflects the varied interests of Horst Herrlich OCo one of the leading category theorists of the world OCo to whom this volume is dedicated in view of his 65th birthday. The book contains applications of categorical methods in various branches of mathematics such as algebra, analysis, logic and topology, as well as fuzzy structures and computer science. At the end of the book the reader will find a complete list of Horst HerrlichOCOs publications. The proceedings have been selected for coverage in: . OCo Index to Scientific & Technical Proceedings- (ISTP- / ISI Proceedings). OCo Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings). OCo CC Proceedings OCo Engineering & Physical Sciences. |
| algebraic structures and their applications: Algebraic Structures and Operators Calculus P. Feinsilver, René Schott, 1993 Introduction I. General remarks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 II. Notations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 III. Lie algebras: some basics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 Chapter 1 Operator calculus and Appell systems I. Boson calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17 II. Holomorphic canonical calculus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 III. Canonical Appell systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23 Chapter 2 Representations of Lie groups I. Coordinates on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 II. Dual representations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 III. Matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 IV. Induced representations and homogeneous spaces . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40 General Appell systems Chapter 3 I. Convolution and stochastic processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44 II. Stochastic processes on Lie groups . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 46 III. Appell systems on Lie groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49 Chapter 4 Canonical systems in several variables I. Homogeneous spaces and Cartan decompositions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 II. Induced representation and coherent states . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62 III. Orthogonal polynomials in several variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 Chapter 5 Algebras with discrete spectrum I. Calculus on groups: review of the theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83 II. Finite-difference algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 III. q-HW algebra and basic hypergeometric functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 IV. su2 and Krawtchouk polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93 V. e2 and Lommel polynomials . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Chapter 6 Nilpotent and solvable algebras I. Heisenberg algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 II. Type-H Lie algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118 Vll III. Upper-triangular matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . 125 IV. Affine and Euclidean algebras . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127 Chapter 7 Hermitian symmetric spaces I. Basic structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 II. Space of rectangular matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 III. Space of skew-symmetric matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 IV. Space of symmetric matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143 Chapter 8 Properties of matrix elements I. Addition formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147 II. Recurrences . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148 III. Quotient representations and summation formulas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 149 Chapter 9 Symbolic computations I. Computing the pi-matrices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 153 II. Adjoint group . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154 III. Recursive computation of matrix elements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . |
| algebraic structures and their applications: Fundamentals of Advanced Mathematics 1 Henri Bourles, 2017-07-10 This precis, comprised of three volumes, of which this book is the first, exposes the mathematical elements which make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. This first volume focuses primarily on algebraic questions: categories and functors, groups, rings, modules and algebra. Notions are introduced in a general framework and then studied in the context of commutative and homological algebra; their application in algebraic topology and geometry is therefore developed. These notions play an essential role in algebraic analysis (analytico-algebraic systems theory of ordinary or partial linear differential equations). The book concludes with a study of modules over the main types of rings, the rational canonical form of matrices, the (commutative) theory of elemental divisors and their application in systems of linear differential equations with constant coefficients. - Part of the New Mathematical Methods, Systems, and Applications series - Presents the notions, results, and proofs necessary to understand and master the various topics - Provides a unified notation, making the task easier for the reader. - Includes several summaries of mathematics for engineers |
| algebraic structures and their applications: Discrete Mathematical Structures and Their Applications Harold S. Stone, 1973 |
| algebraic structures and their applications: From Algebraic Structures to Tensors Gérard Favier, 2020-01-02 Nowadays, tensors play a central role for the representation, mining, analysis, and fusion of multidimensional, multimodal, and heterogeneous big data in numerous fields. This set on Matrices and Tensors in Signal Processing aims at giving a self-contained and comprehensive presentation of various concepts and methods, starting from fundamental algebraic structures to advanced tensor-based applications, including recently developed tensor models and efficient algorithms for dimensionality reduction and parameter estimation. Although its title suggests an orientation towards signal processing, the results presented in this set will also be of use to readers interested in other disciplines. This first book provides an introduction to matrices and tensors of higher-order based on the structures of vector space and tensor space. Some standard algebraic structures are first described, with a focus on the hilbertian approach for signal representation, and function approximation based on Fourier series and orthogonal polynomial series. Matrices and hypermatrices associated with linear, bilinear and multilinear maps are more particularly studied. Some basic results are presented for block matrices. The notions of decomposition, rank, eigenvalue, singular value, and unfolding of a tensor are introduced, by emphasizing similarities and differences between matrices and tensors of higher-order. |
| algebraic structures and their applications: Universal Algebra, Algebraic Logic, and Databases B. Plotkin, 2012-10-12 Modern algebra, which not long ago seemed to be a science divorced from real life, now has numerous applications. Many fine algebraic structures are endowed with meaningful contents. Now and then practice suggests new and unexpected structures enriching algebra. This does not mean that algebra has become merely a tool for applications. Quite the contrary, it significantly benefits from the new connections. The present book is devoted to some algebraic aspects of the theory of databases. It consists of three parts. The first part contains information about universal algebra, algebraic logic is the subject of the second part, and the third one deals with databases. The algebraic material of the flI'St two parts serves the common purpose of applying algebra to databases. The book is intended for use by mathematicians, and mainly by algebraists, who realize the necessity to unite theory and practice. It is also addressed to programmers, engineers and all potential users of mathematics who want to construct their models with the help of algebra and logic. Nowadays, the majority of professional mathematicians work in close cooperation with representatives of applied sciences and even industrial technology. It is neces sary to develop an ability to see mathematics in different particular situations. One of the tasks of this book is to promote the acquisition of such skills. |
| algebraic structures and their applications: Lattices and Ordered Algebraic Structures T.S. Blyth, 2005-04-18 The text can serve as an introduction to fundamentals in the respective areas from a residuated-maps perspective and with an eye on coordinatization. The historical notes that are interspersed are also worth mentioning....The exposition is thorough and all proofs that the reviewer checked were highly polished....Overall, the book is a well-done introduction from a distinct point of view and with exposure to the author’s research expertise. --MATHEMATICAL REVIEWS |
| algebraic structures and their applications: Novel Algebraic Structures Pasquale De Marco, Journey into the captivating world of algebraic structures, where patterns, relationships, and symmetries intertwine to reveal the underlying principles that govern our universe. This comprehensive guidebook invites you to embark on an intellectual adventure, delving into the concepts, properties, and applications of various algebraic structures, including groups, rings, fields, vector spaces, and lattices. With crystal-clear explanations and engaging examples, this book unravels the intricacies of algebraic structures, making them accessible to readers from diverse backgrounds and interests. Discover how these abstract mathematical objects hold the key to understanding a wide range of phenomena, from the motion of planets to the behavior of subatomic particles. Uncover the profound connections between algebra and other branches of mathematics, including number theory, geometry, and topology. Witness the power of algebraic structures in solving complex problems, modeling real-world scenarios, and developing cutting-edge technologies. Through this exploration, you'll gain a deeper appreciation for the elegance and beauty of abstract mathematics. Whether you're a student, a researcher, or simply someone with a passion for knowledge, this book will ignite your curiosity and expand your understanding of the universe we inhabit. Delve into the fascinating world of algebraic structures and uncover the hidden patterns that shape our reality. Embrace the challenge of abstract thinking and unlock the secrets of the mathematical cosmos. Prepare to be amazed by the sheer power and elegance of algebraic structures, and gain a newfound appreciation for the beauty and wonder of mathematics. If you like this book, write a review! |
| algebraic structures and their applications: Recent Advances in Diffeologies and Their Applications Jean-Pierre Magnot, 2024-02-02 This volume contains the proceedings of the AMS-EMS-SMF Special Session on Recent Advances in Diffeologies and Their Applications, held from July 18–20, 2022, at the Université de Grenoble-Alpes, Grenoble, France. The articles present some developments of the theory of diffeologies applied in a broad range of topics, ranging from algebraic topology and higher homotopy theory to integrable systems and optimization in PDE. The geometric framework proposed by diffeologies is known to be one of the most general approaches to problems arising in several areas of mathematics. It can adapt to many contexts without major technical difficulties and produce examples inaccessible by other means, in particular when studying singularities or geometry in infinite dimension. Thanks to this adaptability, diffeologies appear to have become an interesting and useful language for a growing number of mathematicians working in many different fields. Some articles in the volume also illustrate some recent developments of the theory, which makes it even more deep and useful. |
| algebraic structures and their applications: Soft Neutrosophic Algebraic Structures and Their Generalization, Vol. 2 Mumtaz Ali, Florentin Smarandache, Muhammad Shabir, 2014-12-01 In this book, the authors define several new types of soft neutrosophic algebraic structures over neutrosophic algebraic structures and we study their generalizations. These soft neutrosophic algebraic structures are basically parameterized collections of neutrosophic sub-algebraic structures of the neutrosophic algebraic structure. An important feature of this book is that the authors introduce the soft neutrosophic group ring, soft neutrosophic semigroup ring with its generalization, and soft mixed neutrosophic N-algebraic structure over neutrosophic group ring, then the neutrosophic semigroup ring and mixed neutrosophic N-algebraic structure respectively. |
| algebraic structures and their applications: Cluster Algebra Structures on Poisson Nilpotent Algebras K. R Goodearl, M. T. Yakimov, 2023-11-27 View the abstract. |
| algebraic structures and their applications: Fuzzy Sets, Fuzzy Logic and Their Applications Michael Gr. Voskoglou, 2020-03-25 The present book contains 20 articles collected from amongst the 53 total submitted manuscripts for the Special Issue “Fuzzy Sets, Fuzzy Loigic and Their Applications” of the MDPI journal Mathematics. The articles, which appear in the book in the series in which they were accepted, published in Volumes 7 (2019) and 8 (2020) of the journal, cover a wide range of topics connected to the theory and applications of fuzzy systems and their extensions and generalizations. This range includes, among others, management of the uncertainty in a fuzzy environment; fuzzy assessment methods of human-machine performance; fuzzy graphs; fuzzy topological and convergence spaces; bipolar fuzzy relations; type-2 fuzzy; and intuitionistic, interval-valued, complex, picture, and Pythagorean fuzzy sets, soft sets and algebras, etc. The applications presented are oriented to finance, fuzzy analytic hierarchy, green supply chain industries, smart health practice, and hotel selection. This wide range of topics makes the book interesting for all those working in the wider area of Fuzzy sets and systems and of fuzzy logic and for those who have the proper mathematical background who wish to become familiar with recent advances in fuzzy mathematics, which has entered to almost all sectors of human life and activity. |
| algebraic structures and their applications: Collected Papers. Volume VII Florentin Smarandache, 2022-02-01 This seventh volume of Collected Papers includes 70 papers comprising 974 pages on (theoretic and applied) neutrosophics, written between 2013-2021 by the author alone or in collaboration with the following 122 co-authors from 22 countries: Mohamed Abdel-Basset, Abdel-Nasser Hussian, C. Alexander, Mumtaz Ali, Yaman Akbulut, Amir Abdullah, Amira S. Ashour, Assia Bakali, Kousik Bhattacharya, Kainat Bibi, R. N. Boyd, Ümit Budak, Lulu Cai, Cenap Özel, Chang Su Kim, Victor Christianto, Chunlai Du, Chunxin Bo, Rituparna Chutia, Cu Nguyen Giap, Dao The Son, Vinayak Devvrat, Arindam Dey, Partha Pratim Dey, Fahad Alsharari, Feng Yongfei, S. Ganesan, Shivam Ghildiyal, Bibhas C. Giri, Masooma Raza Hashmi, Ahmed Refaat Hawas, Hoang Viet Long, Le Hoang Son, Hongbo Wang, Hongnian Yu, Mihaiela Iliescu, Saeid Jafari, Temitope Gbolahan Jaiyeola, Naeem Jan, R. Jeevitha, Jun Ye, Anup Khan, Madad Khan, Salma Khan, Ilanthenral Kandasamy, W.B. Vasantha Kandasamy, Darjan Karabašević, Kifayat Ullah, Kishore Kumar P.K., Sujit Kumar De, Prasun Kumar Nayak, Malayalan Lathamaheswari, Luong Thi Hong Lan, Anam Luqman, Luu Quoc Dat, Tahir Mahmood, Hafsa M. Malik, Nivetha Martin, Mai Mohamed, Parimala Mani, Mingcong Deng, Mohammed A. Al Shumrani, Mohammad Hamidi, Mohamed Talea, Kalyan Mondal, Muhammad Akram, Muhammad Gulistan, Farshid Mofidnakhaei, Muhammad Shoaib, Muhammad Riaz, Karthika Muthusamy, Nabeela Ishfaq, Deivanayagampillai Nagarajan, Sumera Naz, Nguyen Dinh Hoa, Nguyen Tho Thong, Nguyen Xuan Thao, Noor ul Amin, Dragan Pamučar, Gabrijela Popović, S. Krishna Prabha, Surapati Pramanik, Priya R, Qiaoyan Li, Yaser Saber, Said Broumi, Saima Anis, Saleem Abdullah, Ganeshsree Selvachandran, Abdulkadir Sengür, Seyed Ahmad Edalatpanah, Shahbaz Ali, Shahzaib Ashraf, Shouzhen Zeng, Shio Gai Quek, Shuangwu Zhu, Shumaiza, Sidra Sayed, Sohail Iqbal, Songtao Shao, Sundas Shahzadi, Dragiša Stanujkić, Željko Stević, Udhayakumar Ramalingam, Zunaira Rashid, Hossein Rashmanlou, Rajkumar Verma, Luige Vlădăreanu, Victor Vlădăreanu, Desmond Jun Yi Tey, Selçuk Topal, Naveed Yaqoob, Yanhui Guo, Yee Fei Gan, Yingcang Ma, Young Bae Jun, Yuping Lai, Hafiz Abdul Wahab, Wei Yang, Xiaohong Zhang, Edmundas Kazimieras Zavadskas, Lemnaouar Zedam. |
| algebraic structures and their applications: Engineering Mathematics Exam Study Guide Cybellium, 2024-10-26 Designed for professionals, students, and enthusiasts alike, our comprehensive books empower you to stay ahead in a rapidly evolving digital world. * Expert Insights: Our books provide deep, actionable insights that bridge the gap between theory and practical application. * Up-to-Date Content: Stay current with the latest advancements, trends, and best practices in IT, Al, Cybersecurity, Business, Economics and Science. Each guide is regularly updated to reflect the newest developments and challenges. * Comprehensive Coverage: Whether you're a beginner or an advanced learner, Cybellium books cover a wide range of topics, from foundational principles to specialized knowledge, tailored to your level of expertise. Become part of a global network of learners and professionals who trust Cybellium to guide their educational journey. www.cybellium.com |
| algebraic structures and their applications: Classical Hopf Algebras and Their Applications Pierre Cartier, Frédéric Patras, 2021-09-20 This book is dedicated to the structure and combinatorics of classical Hopf algebras. Its main focus is on commutative and cocommutative Hopf algebras, such as algebras of representative functions on groups and enveloping algebras of Lie algebras, as explored in the works of Borel, Cartier, Hopf and others in the 1940s and 50s. The modern and systematic treatment uses the approach of natural operations, illuminating the structure of Hopf algebras by means of their endomorphisms and their combinatorics. Emphasizing notions such as pseudo-coproducts, characteristic endomorphisms, descent algebras and Lie idempotents, the text also covers the important case of enveloping algebras of pre-Lie algebras. A wide range of applications are surveyed, highlighting the main ideas and fundamental results. Suitable as a textbook for masters or doctoral level programs, this book will be of interest to algebraists and anyone working in one of the fields of application of Hopf algebras. |
| algebraic structures and their applications: Evolution Algebras and Their Applications Jianjun Paul Tian, 2008 Behind genetics and Markov chains, there is an intrinsic algebraic structure. It is defined as a type of new algebra: as evolution algebra. This concept lies between algebras and dynamical systems. Algebraically, evolution algebras are non-associative Banach algebras; dynamically, they represent discrete dynamical systems. Evolution algebras have many connections with other mathematical fields including graph theory, group theory, stochastic processes, dynamical systems, knot theory, 3-manifolds, and the study of the Ihara-Selberg zeta function. In this volume the foundation of evolution algebra theory and applications in non-Mendelian genetics and Markov chains is developed, with pointers to some further research topics. |
| algebraic structures and their applications: Abstract Algebra Thomas Judson, 2023-08-11 Abstract Algebra: Theory and Applications is an open-source textbook that is designed to teach the principles and theory of abstract algebra to college juniors and seniors in a rigorous manner. Its strengths include a wide range of exercises, both computational and theoretical, plus many non-trivial applications. The first half of the book presents group theory, through the Sylow theorems, with enough material for a semester-long course. The second half is suitable for a second semester and presents rings, integral domains, Boolean algebras, vector spaces, and fields, concluding with Galois Theory. |
| algebraic structures and their applications: Information Technologies and Their Applications Gulchohra Mammadova, Telman Aliev, Kamil Aida-zade, 2024-10-16 The two-volume set CCIS 2225 and 2226 constitutes the proceedings of the Second International Conference on Information Technologies and Their Applications, ITTA 2024, held in Baku, Azerbaijan, during April 23-25, 2024. The 51 full papers and 9 short papers presented were carefully reviewed and selected from 200 submissions. They were organized in the following topical sections: Part I - information technology in intelligent systems; and information technology in modeling. Part II - information technology applied in construction, industry, and engineering; and information technology in decision making. |
| algebraic structures and their applications: Algebra in the Stone-Cech Compactification Neil Hindman, Dona Strauss, 2011-12-23 This is the second revised and extended edition of the successful book on the algebraic structure of the Stone-Čech compactification of a discrete semigroup and its combinatorial applications, primarily in the field known as Ramsey Theory. There has been very active research in the subject dealt with by the book in the 12 years which is now included in this edition. This book is a self-contained exposition of the theory of compact right semigroups for discrete semigroups and the algebraic properties of these objects. The methods applied in the book constitute a mosaic of infinite combinatorics, algebra, and topology. The reader will find numerous combinatorial applications of the theory, including the central sets theorem, partition regularity of matrices, multidimensional Ramsey theory, and many more. |
| algebraic structures and their applications: Differential Identities in Rings and Algebras and their Applications Shakir Ali, Mohammad Ashraf, Vincenzo De Filippis, Lahcen Oukhtite, Nadeem Ur Rehman, 2025-05-26 The theory of differential identities in associative rings and algebras is the basis of this monograph. Informally, an identical relation involving arbitrary elements in the underlying rings (or algebras) along with the unknown differential function is called a differential identity in a ring (or algebra). Invariant theory, non-commutative geometry, mathematical physics, and the theory of rings and algebras are just a few of the fields where this abstract theory has proved to be an effective instrument for solving a wide range of challenging issues, and as the twenty-first century has arrived, the theory of differential identities has found enormous applications in resolving a number of unresolved problems in the theory of rings. This volume summarizes the findings and approaches that have significantly advanced the field during the previous three decades. The first chapter provides a brief introduction to the topic. The following three chapters cover the various kinds of derivations in rings and algebras as well as the interactions between the structure of some classes of rings with involution and the behavior of the underlying derivations, generalized derivations, skew derivations, and b-generalized derivations, as well as their corresponding properties. Chapter 5 explores the characterization of several kinds of higher derivable mappings and the structure of Lie and Jordan-type higher derivations. Although the book contains numerous applications of the conclusions presented in these chapters, the last chapter mostly focuses on the application of derivations. This research monograph is useful for researchers working in the area of differential identities in rings and algebras. It provides a comprehensive and authoritative account of research findings. |
| algebraic structures and their applications: Fourier Analysis on Finite Groups with Applications in Signal Processing and System Design Radomir S. Stankovic, Claudio Moraga, Jaakko Astola, 2005-08-08 Discover applications of Fourier analysis on finite non-Abeliangroups The majority of publications in spectral techniques considerFourier transform on Abelian groups. However, non-Abelian groupsprovide notable advantages in efficient implementations of spectralmethods. Fourier Analysis on Finite Groups with Applications in SignalProcessing and System Design examines aspects of Fourieranalysis on finite non-Abelian groups and discusses differentmethods used to determine compact representations for discretefunctions providing for their efficient realizations and relatedapplications. Switching functions are included as an example ofdiscrete functions in engineering practice. Additionally,consideration is given to the polynomial expressions and decisiondiagrams defined in terms of Fourier transform on finitenon-Abelian groups. A solid foundation of this complex topic is provided bybeginning with a review of signals and their mathematical modelsand Fourier analysis. Next, the book examines recent achievementsand discoveries in: Matrix interpretation of the fast Fourier transform Optimization of decision diagrams Functional expressions on quaternion groups Gibbs derivatives on finite groups Linear systems on finite non-Abelian groups Hilbert transform on finite groups Among the highlights is an in-depth coverage of applications ofabstract harmonic analysis on finite non-Abelian groups in compactrepresentations of discrete functions and related tasks in signalprocessing and system design, including logic design. All chaptersare self-contained, each with a list of references to facilitatethe development of specialized courses or self-study. With nearly 100 illustrative figures and fifty tables, this isan excellent textbook for graduate-level students and researchersin signal processing, logic design, and system theory-as well asthe more general topics of computer science and appliedmathematics. |
Algebra - Wikipedia
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of …
Algebraic Expression - Definition, Examples, Parts, & Formulas
May 30, 2024 · Algebraic expression, or variable expression, is a mathematical expression consisting of two main parts, variables and constants, joined together using mathematical …
ALGEBRAIC | English meaning - Cambridge Dictionary
Quantitative, algebraic reasoning lies behind modern economics. I’m looking for a font on my computer with standard algebraic symbols. The same algebraic equations that predict the size …
ALGEBRAIC Definition & Meaning - Merriam-Webster
The meaning of ALGEBRAIC is relating to, involving, or according to the laws of algebra. How to use algebraic in a sentence.
Khan Academy
Learn algebra—variables, equations, functions, graphs, and more.
Algebraic - definition of algebraic by The Free Dictionary
Define algebraic. algebraic synonyms, algebraic pronunciation, algebraic translation, English dictionary definition of algebraic. adj. 1. Of, relating to, or designating algebra. 2. Designating …
1.4: Algebraic Expressions and Formulas - Mathematics LibreTexts
Oct 6, 2021 · Identify the parts of an algebraic expression. Apply the distributive property. Evaluate algebraic expressions. Use formulas that model common applications.
ALGEBRAIC Definition & Meaning - Dictionary.com
Mathematics. of or relating to an element that is the root of a polynomial equation with coefficients from some given field. is algebraic over the field of real numbers. using arbitrary letters or …
Algebraic Expressions in Math: Definition, Example and Equation
Apr 11, 2025 · Algebraic Expression is a mathematical expression that is made of numbers, and variables connected with any arithmetical operation between them. Algebraic forms are used …
What is Algebra? Definition, Basics, Examples, Facts - SplashLearn
Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions. In algebra, we use numbers like 2, −7, 0.068 etc., which have a …
Algebra - Wikipedia
Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of …
Algebraic Expression - Definition, Examples, Parts, & Formulas
May 30, 2024 · Algebraic expression, or variable expression, is a mathematical expression consisting of two main parts, variables and constants, joined together using mathematical …
ALGEBRAIC | English meaning - Cambridge Dictionary
Quantitative, algebraic reasoning lies behind modern economics. I’m looking for a font on my computer with standard algebraic symbols. The same algebraic equations that predict the size …
ALGEBRAIC Definition & Meaning - Merriam-Webster
The meaning of ALGEBRAIC is relating to, involving, or according to the laws of algebra. How to use algebraic in a sentence.
Khan Academy
Learn algebra—variables, equations, functions, graphs, and more.
Algebraic - definition of algebraic by The Free Dictionary
Define algebraic. algebraic synonyms, algebraic pronunciation, algebraic translation, English dictionary definition of algebraic. adj. 1. Of, relating to, or designating algebra. 2. Designating …
1.4: Algebraic Expressions and Formulas - Mathematics LibreTexts
Oct 6, 2021 · Identify the parts of an algebraic expression. Apply the distributive property. Evaluate algebraic expressions. Use formulas that model common applications.
ALGEBRAIC Definition & Meaning - Dictionary.com
Mathematics. of or relating to an element that is the root of a polynomial equation with coefficients from some given field. is algebraic over the field of real numbers. using arbitrary letters or …
Algebraic Expressions in Math: Definition, Example and Equation
Apr 11, 2025 · Algebraic Expression is a mathematical expression that is made of numbers, and variables connected with any arithmetical operation between them. Algebraic forms are used …
What is Algebra? Definition, Basics, Examples, Facts - SplashLearn
Algebra is the part of mathematics that helps represent problems or situations in the form of mathematical expressions. In algebra, we use numbers like 2, −7, 0.068 etc., which have a …
