Boolean Constructions In Universal Algebras

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Boolean Constructions In Universal Algebras

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Author : A. G. Pinus
language : en
Publisher:
Release Date : 2014-01-15

Boolean Constructions In Universal Algebras written by A. G. Pinus and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.

Boolean Constructions In Universal Algebras

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Author : A.G. Pinus
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Boolean Constructions In Universal Algebras written by A.G. Pinus 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 2013-04-17 with Mathematics categories.

During the last few decades the ideas, methods, and results of the theory of Boolean algebras have played an increasing role in various branches of mathematics and cybernetics. This monograph is devoted to the fundamentals of the theory of Boolean constructions in universal algebra. Also considered are the problems of presenting different varieties of universal algebra with these constructions, and applications for investigating the spectra and skeletons of varieties of universal algebras. For researchers whose work involves universal algebra and logic.

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.

Universal Algebra And Coalgebra

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Author : Klaus Denecke
language : en
Publisher: World Scientific
Release Date : 2009

Universal Algebra And Coalgebra written by Klaus Denecke and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Mathematics categories.

The purpose of this book is to study the structures needed to model objects in universal algebra, universal coalgebra and theoretical computer science. Universal algebra is used to describe different kinds of algebraic structures, while coalgebras are used to model state-based machines in computer science.The connection between algebras and coalgebras provides a way to connect static data-oriented systems with dynamical behavior-oriented systems. Algebras are used to describe data types and coalgebras describe abstract systems or machines.The book presents a clear overview of the area, from which further study may proceed.

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.

Decidability And Boolean Representations

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Author : Stanley Burris
language : en
Publisher: American Mathematical Soc.
Release Date : 1981

Decidability And Boolean Representations written by Stanley Burris and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1981 with Mathematics categories.

In part I we address the question: which varieties have a decidable first order theory? We confine our attention to varieties whose algebras have modular congruence lattices (i.e., modular varieties), and focus primarily on locally finite varieties, although near the end of the paper Zamjatin's description of all decidable varieties of groups and rings, and offer a new proof of it. In part II, we show that if a variety admits such sheaf representations using only finitely many stalks, all of which are finite, then the variety can be decomposed in the product of a discriminator variety and an abelian variety. We continue this investigation by looking at well-known specializations of the sheaf construction, namely Boolean powers and sub-Boolean powers, giving special emphasis to quasi-primal algebras A, such that the sub-Boolean powers of A form a variety (this extends the work of Arens and Kaplansky on finite fields).

Universal Algebra

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Author : Clifford Bergman
language : en
Publisher: CRC Press
Release Date : 2011-09-20

Universal Algebra written by Clifford Bergman and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-09-20 with Computers categories.

Starting with the most basic notions, Universal Algebra: Fundamentals and Selected Topics introduces all the key elements needed to read and understand current research in this field. Based on the author’s two-semester course, the text prepares students for research work by providing a solid grounding in the fundamental constructions and concepts of universal algebra and by introducing a variety of recent research topics. The first part of the book focuses on core components, including subalgebras, congruences, lattices, direct and subdirect products, isomorphism theorems, a clone of operations, terms, free algebras, Birkhoff’s theorem, and standard Maltsev conditions. The second part covers topics that demonstrate the power and breadth of the subject. The author discusses the consequences of Jónsson’s lemma, finitely and nonfinitely based algebras, definable principal congruences, and the work of Foster and Pixley on primal and quasiprimal algebras. He also includes a proof of Murskiĭ’s theorem on primal algebras and presents McKenzie’s characterization of directly representable varieties, which clearly shows the power of the universal algebraic toolbox. The last chapter covers the rudiments of tame congruence theory. Throughout the text, a series of examples illustrates concepts as they are introduced and helps students understand how universal algebra sheds light on topics they have already studied, such as Abelian groups and commutative rings. Suitable for newcomers to the field, the book also includes carefully selected exercises that reinforce the concepts and push students to a deeper understanding of the theorems and techniques.

Sheaves Of Algebras Over Boolean Spaces

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Author : Arthur Knoebel
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-12-15

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 2011-12-15 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.

Universal Algebra And Lattice Theory

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Author : R.S. Freese
language : en
Publisher: Springer
Release Date : 2006-11-15

Universal Algebra And Lattice Theory written by R.S. Freese and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Countable Boolean Algebras And Decidability

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Author : Sergey Goncharov
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-01-31

Countable Boolean Algebras And Decidability written by Sergey Goncharov 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 1997-01-31 with Mathematics categories.

This book describes the latest Russian research covering the structure and algorithmic properties of Boolean algebras from the algebraic and model-theoretic points of view. A significantly revised version of the author's Countable Boolean Algebras (Nauka, Novosibirsk, 1989), the text presents new results as well as a selection of open questions on Boolean algebras. Other current features include discussions of the Kottonen algebras in enrichments by ideals and automorphisms, and the properties of the automorphism groups.