An Invitation To General Algebra And Universal Constructions
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An Invitation To General Algebra And Universal Constructions
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Author : George M. Bergman
language : en
Publisher: Springer
Release Date : 2015-02-05
An Invitation To General Algebra And Universal Constructions written by George M. Bergman and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-05 with Mathematics categories.
Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
Hyperidentities Boolean And De Morgan Structures
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Author : Yuri Movsisyan
language : en
Publisher: World Scientific
Release Date : 2022-09-20
Hyperidentities Boolean And De Morgan Structures written by Yuri Movsisyan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-20 with Mathematics categories.
Hyperidentities are important formulae of second-order logic, and research in hyperidentities paves way for the study of second-order logic and second-order model theory.This book illustrates many important current trends and perspectives for the field of hyperidentities and their applications, of interest to researchers in modern algebra and discrete mathematics. It covers a number of directions, including the characterizations of the Boolean algebra of n-ary Boolean functions and the distributive lattice of n-ary monotone Boolean functions; the classification of hyperidentities of the variety of lattices, the variety of distributive (modular) lattices, the variety of Boolean algebras, and the variety of De Morgan algebras; the characterization of algebras with aforementioned hyperidentities; the functional representations of finitely-generated free algebras of various varieties of lattices and bilattices via generalized Boolean functions (De Morgan functions, quasi-De Morgan functions, super-Boolean functions, super-De Morgan functions, etc); the structural results for De Morgan algebras, Boole-De Morgan algebras, super-Boolean algebras, bilattices, among others.While problems of Boolean functions theory are well known, the present book offers alternative, more general problems, involving the concepts of De Morgan functions, quasi-De Morgan functions, super-Boolean functions, and super-De Morgan functions, etc. In contrast to other generalized Boolean functions discovered and investigated so far, these functions have clearly normal forms. This quality is of crucial importance for their applications in pure and applied mathematics, especially in discrete mathematics, quantum computation, quantum information theory, quantum logic, and the theory of quantum computers.
Pillars Of Computer Science
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Author : Arnon Avron
language : en
Publisher: Springer
Release Date : 2008-02-08
Pillars Of Computer Science written by Arnon Avron and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-08 with Computers categories.
For over half a century, Boris (Boaz) Trakhtenbrot has made seminal contributions to virtually all of the central areas of theoretical computer science. This festschrift volume readily illustrates the profound influence he has had on the field.
Positivity And Its Applications
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Author : Eder Kikianty
language : en
Publisher: Springer Nature
Release Date : 2021-07-22
Positivity And Its Applications written by Eder Kikianty and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-22 with Mathematics categories.
This proceedings volume features selected contributions from the conference Positivity X. The field of positivity deals with ordered mathematical structures and their applications. At the biannual series of Positivity conferences, the latest developments in this diverse field are presented. The 2019 edition was no different, with lectures covering a broad spectrum of topics, including vector and Banach lattices and operators on such spaces, abstract stochastic processes in an ordered setting, the theory and applications of positive semi-groups to partial differential equations, Hilbert geometries, positivity in Banach algebras and, in particular, operator algebras, as well as applications to mathematical economics and financial mathematics. The contributions in this book reflect the variety of topics discussed at the conference. They will be of interest to researchers in functional analysis, operator theory, measure and integration theory, operator algebras, and economics. Positivity X was dedicated to the memory of our late colleague and friend, Coenraad Labuschagne. His untimely death in 2018 came as an enormous shock to the Positivity community. He was a prominent figure in the Positivity community and was at the forefront of the recent development of abstract stochastic processes in a vector lattice context.
Csu Abstract Algebra
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Author :
language : en
Publisher: PediaPress
Release Date :
Csu Abstract Algebra written by and has been published by PediaPress this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Algebras Lattices Varieties
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Author : Ralph S. Freese
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-03
Algebras Lattices Varieties written by Ralph S. Freese and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-03 with Mathematics categories.
This book is the third of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.
Recent Trends In Algebraic Development Techniques
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Author : Markus Roggenbach
language : en
Publisher: Springer Nature
Release Date : 2021-04-10
Recent Trends In Algebraic Development Techniques written by Markus Roggenbach and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-04-10 with Computers categories.
This book constitutes the thoroughly refereed post-conference proceedings of the 25th International Workshop on Algebraic Development Techniques, WADT 2020, held virtually in April 2020. The 7 revised papers presented together with an invited paper were carefully reviewed and selected from 9 submissions. The contributed presentations covered a range of topics about the algebraic approach to system specification, which encompasses many aspects of the formal design of software systems. Originally born as formal method for reasoning about abstract data types, the algebraic approach now covers new specification frameworks and programming paradigms (such as object-oriented, aspect-oriented, agent-oriented, logic, and higher-order functional programming) as well as a wide range of application areas (including information systems, concurrent, distributed, and mobile systems).
Approximations And Endomorphism Algebras Of Modules
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Author : Rüdiger Göbel
language : en
Publisher: Walter de Gruyter
Release Date : 2012-10-01
Approximations And Endomorphism Algebras Of Modules written by Rüdiger Göbel and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-01 with Mathematics categories.
This second, revised and substantially extended edition of Approximations and Endomorphism Algebras of Modules reflects both the depth and the width of recent developments in the area since the first edition appeared in 2006. The new division of the monograph into two volumes roughly corresponds to its two central topics, approximation theory (Volume 1) and realization theorems for modules (Volume 2). It is a widely accepted fact that the category of all modules over a general associative ring is too complex to admit classification. Unless the ring is of finite representation type we must limit attempts at classification to some restricted subcategories of modules. The wild character of the category of all modules, or of one of its subcategories C, is often indicated by the presence of a realization theorem, that is, by the fact that any reasonable algebra is isomorphic to the endomorphism algebra of a module from C. This results in the existence of pathological direct sum decompositions, and these are generally viewed as obstacles to classification. In order to overcome this problem, the approximation theory of modules has been developed. The idea here is to select suitable subcategories C whose modules can be classified, and then to approximate arbitrary modules by those from C. These approximations are neither unique nor functorial in general, but there is a rich supply available appropriate to the requirements of various particular applications. The authors bring the two theories together. The first volume, Approximations, sets the scene in Part I by introducing the main classes of modules relevant here: the S-complete, pure-injective, Mittag-Leffler, and slender modules. Parts II and III of the first volume develop the key methods of approximation theory. Some of the recent applications to the structure of modules are also presented here, notably for tilting, cotilting, Baer, and Mittag-Leffler modules. In the second volume, Predictions, further basic instruments are introduced: the prediction principles, and their applications to proving realization theorems. Moreover, tools are developed there for answering problems motivated in algebraic topology. The authors concentrate on the impossibility of classification for modules over general rings. The wild character of many categories C of modules is documented here by the realization theorems that represent critical R-algebras over commutative rings R as endomorphism algebras of modules from C. The monograph starts from basic facts and gradually develops the theory towards its present frontiers. It is suitable both for graduate students interested in algebra and for experts in module and representation theory.
Sheaves Of Algebras Over Boolean Spaces
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Author : Arthur Knoebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-16
Sheaves Of Algebras Over Boolean Spaces written by Arthur Knoebel and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-12-16 with Mathematics categories.
This unique monograph building bridges among a number of different areas of mathematics such as algebra, topology, and category theory. The author uses various tools to develop new applications of classical concepts. Detailed proofs are given for all major theorems, about half of which are completely new. Sheaves of Algebras over Boolean Spaces will take readers on a journey through sheaf theory, an important part of universal algebra. This excellent reference text is suitable for graduate students, researchers, and those who wish to learn about sheaves of algebras.
Algebras Lattices Varieties
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Author : Ralph N. McKenzie
language : en
Publisher: American Mathematical Society
Release Date : 2018-07-09
Algebras Lattices Varieties written by Ralph N. McKenzie and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-07-09 with Mathematics categories.
This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text.