Noetherian Semigroup Algebras
Noetherian Semigroup Algebras

Author: Eric Jespers

Publisher: Springer Science & Business Media

Published: 2007-03-15

Total Pages: 364

ISBN-13: 1402058101

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Here is a comprehensive treatment of the main results and methods of the theory of Noetherian semigroup algebras. These results are applied and illustrated in the context of important classes of algebras that arise in a variety of areas and have recently been intensively studied. The focus is on the interplay between combinatorics and algebraic structure. Mathematical physicists will find this work interesting for its attention to applications of the Yang-Baxter equation.

Semigroup Algebras
Semigroup Algebras

Author: Jan Okninski

Publisher: CRC Press

Published: 2020-08-27

Total Pages: 288

ISBN-13: 1000147665

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Gathers and unifies the results of the theory of noncommutative semigroup rings, primarily drawing on the literature of the last 10 years, and including several new results. Okninski (Warsaw U., Poland) restricts coverage to the ring theoretical properties for which a systematic treatment is current

Interactions Between Ring Theory and Representations of Algebras
Interactions Between Ring Theory and Representations of Algebras

Author: Freddy Van Oystaeyen

Publisher: CRC Press

Published: 2000-04-05

Total Pages: 470

ISBN-13: 9780824703677

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This work is based on a set of lectures and invited papers presented at a meeting in Murcia, Spain, organized by the European Commission's Training and Mobility of Researchers (TMR) Programme. It contains information on the structure of representation theory of groups and algebras and on general ring theoretic methods related to the theory.

Multiplicative Ideal Theory and Factorization Theory
Multiplicative Ideal Theory and Factorization Theory

Author: Scott Chapman

Publisher: Springer

Published: 2016-07-29

Total Pages: 414

ISBN-13: 331938855X

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This book consists of both expository and research articles solicited from speakers at the conference entitled "Arithmetic and Ideal Theory of Rings and Semigroups," held September 22–26, 2014 at the University of Graz, Graz, Austria. It reflects recent trends in multiplicative ideal theory and factorization theory, and brings together for the first time in one volume both commutative and non-commutative perspectives on these areas, which have their roots in number theory, commutative algebra, and algebraic geometry. Topics discussed include topological aspects in ring theory, Prüfer domains of integer-valued polynomials and their monadic submonoids, and semigroup algebras. It will be of interest to practitioners of mathematics and computer science, and researchers in multiplicative ideal theory, factorization theory, number theory, and algebraic geometry.

Groups, Rings, Lie and Hopf Algebras
Groups, Rings, Lie and Hopf Algebras

Author: Y. Bahturin

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 240

ISBN-13: 1461302358

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The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Groups, Rings, Lie and Hopf Algebras
Groups, Rings, Lie and Hopf Algebras

Author:

Publisher: Springer Science & Business Media

Published: 2003-03-31

Total Pages: 266

ISBN-13: 9781402012204

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The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial University of Newfoundland, St. John's, NF, Canada. All four areas from the title of the workshop are covered. In addition, some chapters touch upon the topics, which belong to two or more areas at the same time. Audience: The readership targeted includes researchers, graduate and senior undergraduate students in mathematics and its applications.

Algebra - Representation Theory
Algebra - Representation Theory

Author: Klaus W. Roggenkamp

Publisher: Springer Science & Business Media

Published: 2001-08-31

Total Pages: 488

ISBN-13: 9780792371137

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Over the last three decades representation theory of groups, Lie algebras and associative algebras has undergone a rapid development through the powerful tool of almost split sequences and the Auslander-Reiten quiver. Further insight into the homology of finite groups has illuminated their representation theory. The study of Hopf algebras and non-commutative geometry is another new branch of representation theory which pushes the classical theory further. All this can only be seen in connection with an understanding of the structure of special classes of rings. The aim of this book is to introduce the reader to some modern developments in: Lie algebras, quantum groups, Hopf algebras and algebraic groups; non-commutative algebraic geometry; representation theory of finite groups and cohomology; the structure of special classes of rings.

Ring Constructions and Applications
Ring Constructions and Applications

Author: Andrei V. Kelarev

Publisher: World Scientific

Published: 2002

Total Pages: 218

ISBN-13: 9810247451

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This book contains the definitions of several ring constructions used in various applications. The concept of a groupoid-graded ring includes many of these constructions as special cases and makes it possible to unify the exposition. Recent research results on groupoid-graded rings and more specialized constructions are presented. In addition, there is a chapter containing open problems currently considered in the literature. Ring Constructions and Applications can serve as an excellent introduction for graduate students to many ring constructions as well as to essential basic concepts of group, semigroup and ring theories used in proofs.

Semigroups Of Matrices
Semigroups Of Matrices

Author: Jan Okninski

Publisher: World Scientific

Published: 1998-07-31

Total Pages: 327

ISBN-13: 981449626X

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This book is concerned with the structure of linear semigroups, that is, subsemigroups of the multiplicative semigroup Mn(K) of n × n matrices over a field K (or, more generally, skew linear semigroups — if K is allowed to be a division ring) and its applications to certain problems on associative algebras, semigroups and linear representations. It is motivated by several recent developments in the area of linear semigroups and their applications. It summarizes the state of knowledge in this area, presenting the results for the first time in a unified form. The book's point of departure is a structure theorem, which allows the use of powerful techniques of linear groups. Certain aspects of a combinatorial nature, connections with the theory of linear representations and applications to various problems on associative algebras are also discussed.

Multiplicative Ideal Theory in Commutative Algebra
Multiplicative Ideal Theory in Commutative Algebra

Author: James W. Brewer

Publisher: Springer Science & Business Media

Published: 2006-12-15

Total Pages: 437

ISBN-13: 0387367179

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This volume, a tribute to the work of Robert Gilmer, consists of twenty-four articles authored by his most prominent students and followers. These articles combine surveys of past work by Gilmer and others, recent results which have never before seen print, open problems, and extensive bibliographies. The entire collection provides an in-depth overview of the topics of research in a significant and large area of commutative algebra.