Semigroups, Categories, and Partial Algebras
Semigroups, Categories, and Partial Algebras

Author: P. G. Romeo

Publisher: Springer Nature

Published: 2021-03-26

Total Pages: 249

ISBN-13: 9813348429

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This book is a collection of selected papers presented at the International Conference on Semigroups and Applications, held at the Cochin University of Science and Technology, India, from December 9–12, 2019. This book discusses the recent developments in semigroups theory, category theory and the applications of these in various areas of research, including structure theory of semigroups, lattices, rings and partial algebras. This book presents chapters on ordering orders and quotient rings, block groups and Hall’s relations, quotients of the Booleanization of inverse semigroup, Markov chains through semigroup graph expansions, polycyclic inverse monoids and Thompson group, balanced category and bundle category. This book will be of much value to researchers working in areas of semigroup and operator theory.

Semigroups, Categories, and Partial Algebras
Semigroups, Categories, and Partial Algebras

Author: P. G. Romeo

Publisher:

Published: 2021

Total Pages: 241

ISBN-13: 9789813348431

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This book is a collection of selected papers presented at the International Conference on Semigroups and Applications, held at the Cochin University of Science and Technology, India, from December 9-12, 2019. This book discusses the recent developments in semigroups theory, category theory and the applications of these in various areas of research, including structure theory of semigroups, lattices, rings and partial algebras. This book presents chapters on ordering orders and quotient rings, block groups and Hall's relations, quotients of the Booleanization of inverse semigroup, Markov chains through semigroup graph expansions, polycyclic inverse monoids and Thompson group, balanced category and bundle category. This book will be of much value to researchers working in areas of semigroup and operator theory.

Nineteen Papers on Algebraic Semigroups
Nineteen Papers on Algebraic Semigroups

Author: Ben Silver

Publisher: American Mathematical Soc.

Published: 1988-12-31

Total Pages: 224

ISBN-13: 9780821895757

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This volume contains papers selected by leading specialists in algebraic semigroups in the U.S., the United Kingdom, and Australia. Many of the papers strongly influenced the development of algebraic semigroups, but most were virtually unavailable outside the U.S.S.R. Written by some of the most prominent Soviet researchers in the field, the papers have a particular emphasis on semigroups of transformations. Boris Schein of the University of Arkansas is the translator.

Finite Semigroups and Universal Algebra
Finite Semigroups and Universal Algebra

Author: Jorge Almeida

Publisher: World Scientific

Published: 1994

Total Pages: 540

ISBN-13: 9789810218959

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Motivated by applications in theoretical computer science, the theory of finite semigroups has emerged in recent years as an autonomous area of mathematics. It fruitfully combines methods, ideas and constructions from algebra, combinatorics, logic and topology. In simple terms, the theory aims at a classification of finite semigroups in certain classes called ?pseudovarieties?. The classifying characteristics have both structural and syntactical aspects, the general connection between them being part of universal algebra. Besides providing a foundational study of the theory in the setting of arbitrary abstract finite algebras, this book stresses the syntactical approach to finite semigroups. This involves studying (relatively) free and profinite free semigroups and their presentations. The techniques used are illustrated in a systematic study of various operators on pseudovarieties of semigroups.

Partial Dynamical Systems, Fell Bundles and Applications
Partial Dynamical Systems, Fell Bundles and Applications

Author: Ruy Exel

Publisher: American Mathematical Soc.

Published: 2017-09-20

Total Pages: 330

ISBN-13: 1470437856

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Partial dynamical systems, originally developed as a tool to study algebras of operators in Hilbert spaces, has recently become an important branch of algebra. Its most powerful results allow for understanding structural properties of algebras, both in the purely algebraic and in the C*-contexts, in terms of the dynamical properties of certain systems which are often hiding behind algebraic structures. The first indication that the study of an algebra using partial dynamical systems may be helpful is the presence of a grading. While the usual theory of graded algebras often requires gradings to be saturated, the theory of partial dynamical systems is especially well suited to treat nonsaturated graded algebras which are in fact the source of the notion of “partiality”. One of the main results of the book states that every graded algebra satisfying suitable conditions may be reconstructed from a partial dynamical system via a process called the partial crossed product. Running in parallel with partial dynamical systems, partial representations of groups are also presented and studied in depth. In addition to presenting main theoretical results, several specific examples are analyzed, including Wiener–Hopf algebras and graph C*-algebras.

Homological Algebra: The Interplay Of Homology With Distributive Lattices And Orthodox Semigroups
Homological Algebra: The Interplay Of Homology With Distributive Lattices And Orthodox Semigroups

Author: Marco Grandis

Publisher: World Scientific

Published: 2012-06-08

Total Pages: 382

ISBN-13: 9814407089

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In this book we want to explore aspects of coherence in homological algebra, that already appear in the classical situation of abelian groups or abelian categories. Lattices of subobjects are shown to play an important role in the study of homological systems, from simple chain complexes to all the structures that give rise to spectral sequences. A parallel role is played by semigroups of endorelations.These links rest on the fact that many such systems, but not all of them, live in distributive sublattices of the modular lattices of subobjects of the system.The property of distributivity allows one to work with induced morphisms in an automatically consistent way, as we prove in a ‘Coherence Theorem for homological algebra’. (On the contrary, a ‘non-distributive’ homological structure like the bifiltered chain complex can easily lead to inconsistency, if one explores the interaction of its two spectral sequences farther than it is normally done.)The same property of distributivity also permits representations of homological structures by means of sets and lattices of subsets, yielding a precise foundation for the heuristic tool of Zeeman diagrams as universal models of spectral sequences.We thus establish an effective method of working with spectral sequences, called ‘crossword chasing’, that can often replace the usual complicated algebraic tools and be of much help to readers that want to apply spectral sequences in any field.

Operads and Universal Algebra
Operads and Universal Algebra

Author: Chengming Bai

Publisher: World Scientific

Published: 2012

Total Pages: 318

ISBN-13: 9814365114

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The book aims to exemplify the recent developments in operad theory, in universal algebra and related topics in algebraic topology and theoretical physics. The conference has established a better connection between mathematicians working on operads (mainly the French team) and mathematicians working in universal algebra (primarily the Chinese team), and to exchange problems, methods and techniques from these two subject areas.

Algebras and Orders
Algebras and Orders

Author: Ivo G. Rosenberg

Publisher: Springer Science & Business Media

Published: 2013-03-09

Total Pages: 565

ISBN-13: 9401706972

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In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.