Advances In Rings And Modules

Author : Sergio R. López-Permouth,Dinh Van Huynh
Publisher : Springer Science & Business Media
Page : 345 pages
File Size : 54,9 Mb
Release : 2011-01-28
Category : Mathematics
ISBN : 9783034602860

Get Book

Advances in Ring Theory by Sergio R. López-Permouth,Dinh Van Huynh Pdf

This volume consists of refereed research and expository articles by both plenary and other speakers at the International Conference on Algebra and Applications held at Ohio University in June 2008, to honor S.K. Jain on his 70th birthday. The articles are on a wide variety of areas in classical ring theory and module theory, such as rings satisfying polynomial identities, rings of quotients, group rings, homological algebra, injectivity and its generalizations, etc. Included are also applications of ring theory to problems in coding theory and in linear algebra.

Author : Sergio R. López-Permouth,Jae Keol Park,S. Tariq Rizvi,Cosmin S. Roman
Publisher : American Mathematical Soc.
Page : 283 pages
File Size : 55,9 Mb
Release : 2018-09-06
Category : Modules (Algebra)
ISBN : 9781470435554

Get Book

Advances in Rings and Modules by Sergio R. López-Permouth,Jae Keol Park,S. Tariq Rizvi,Cosmin S. Roman Pdf

This volume, dedicated to Bruno J. Müller, a renowned algebraist, is a collection of papers that provide a snapshot of the diversity of themes and applications that interest algebraists today. The papers highlight the latest progress in ring and module research and present work done on the frontiers of the topics discussed. In addition, selected expository articles are included to give algebraists and other mathematicians, including graduate students, an accessible introduction to areas that may be outside their own expertise.

Author : Alberto Facchini,Marco Fontana,Alfred Geroldinger,Bruce Olberding
Publisher : Springer Nature
Page : 341 pages
File Size : 47,6 Mb
Release : 2020-06-02
Category : Mathematics
ISBN : 9783030434168

Get Book

Advances in Rings, Modules and Factorizations by Alberto Facchini,Marco Fontana,Alfred Geroldinger,Bruce Olberding Pdf

Occasioned by the international conference "Rings and Factorizations" held in February 2018 at University of Graz, Austria, this volume represents a wide range of research trends in the theory of commutative and non-commutative rings and their modules, including multiplicative ideal theory, Dedekind and Krull rings and their generalizations, rings of integer valued-polynomials, topological aspects of ring theory, factorization theory in rings and semigroups and direct-sum decompositions of modules. The volume will be of interest to researchers seeking to extend or utilize work in these areas as well as graduate students wishing to find entryways into active areas of current research in algebra. A novel aspect of the volume is an emphasis on how diverse types of algebraic structures and contexts (rings, modules, semigroups, categories) may be treated with overlapping and reinforcing approaches.

Author : S.K. Jain,Rizvi S. Tariq
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 45,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461219781

Get Book

Advances in Ring Theory by S.K. Jain,Rizvi S. Tariq Pdf

Author : Gary F. Birkenmeier,Jae Keol Park,S Tariq Rizvi
Publisher : Springer Science & Business Media
Page : 442 pages
File Size : 48,7 Mb
Release : 2013-07-19
Category : Mathematics
ISBN : 9780387927169

Get Book

Extensions of Rings and Modules by Gary F. Birkenmeier,Jae Keol Park,S Tariq Rizvi Pdf

The "extensions" of rings and modules have yet to be explored in detail in a research monograph. This book presents state of the art research and also stimulating new and further research. Broken into three parts, Part I begins with basic notions, terminology, definitions and a description of the classes of rings and modules. Part II considers the transference of conditions between a base ring or module and its extensions. And Part III utilizes the concept of a minimal essental extension with respect to a specific class (a hull). Mathematical interdisciplinary applications appear throughout. Major applications of the ring and module theory to Functional Analysis, especially C*-algebras, appear in Part III, make this book of interest to Algebra and Functional Analysis researchers. Notes and exercises at the end of every chapter, and open problems at the end of all three parts, lend this as an ideal textbook for graduate or advanced undergradate students.

Author : Frank W. Anderson,Kent R. Fuller
Publisher : Springer Science & Business Media
Page : 386 pages
File Size : 50,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461244189

Get Book

Rings and Categories of Modules by Frank W. Anderson,Kent R. Fuller Pdf

This book is intended to provide a reasonably self-contained account of a major portion of the general theory of rings and modules suitable as a text for introductory and more advanced graduate courses. We assume the famil iarity with rings usually acquired in standard undergraduate algebra courses. Our general approach is categorical rather than arithmetical. The continuing theme of the text is the study of the relationship between the one-sided ideal structure that a ring may possess and the behavior of its categories of modules. Following a brief outline of set-theoretic and categorical foundations, the text begins with the basic definitions and properties of rings, modules and homomorphisms and ranges through comprehensive treatments of direct sums, finiteness conditions, the Wedderburn-Artin Theorem, the Jacobson radical, the hom and tensor functions, Morita equivalence and duality, de composition theory of injective and projective modules, and semi perfect and perfect rings. In this second edition we have included a chapter containing many of the classical results on artinian rings that have hdped to form the foundation for much of the contemporary research on the representation theory of artinian rings and finite dimensional algebras. Both to illustrate the text and to extend it we have included a substantial number of exercises covering a wide spectrum of difficulty. There are, of course" many important areas of ring and module theory that the text does not touch upon.

Author : A. J. Berrick,M. E. Keating
Publisher : Cambridge University Press
Page : 286 pages
File Size : 52,5 Mb
Release : 2000-05
Category : Mathematics
ISBN : 0521632749

Get Book

An Introduction to Rings and Modules by A. J. Berrick,M. E. Keating Pdf

This is a concise 2000 introduction at graduate level to ring theory, module theory and number theory.

Author : Marco Fontana,Sophie Frisch,Sarah Glaz,Francesca Tartarone,Paolo Zanardo
Publisher : Springer
Page : 375 pages
File Size : 49,7 Mb
Release : 2017-11-11
Category : Mathematics
ISBN : 9783319658742

Get Book

Rings, Polynomials, and Modules by Marco Fontana,Sophie Frisch,Sarah Glaz,Francesca Tartarone,Paolo Zanardo Pdf

This volume presents a collection of articles highlighting recent developments in commutative algebra and related non-commutative generalizations. It also includes an extensive bibliography and lists a substantial number of open problems that point to future directions of research in the represented subfields. The contributions cover areas in commutative algebra that have flourished in the last few decades and are not yet well represented in book form. Highlighted topics and research methods include Noetherian and non-Noetherian ring theory, module theory and integer-valued polynomials along with connections to algebraic number theory, algebraic geometry, topology and homological algebra. Most of the eighteen contributions are authored by attendees of the two conferences in commutative algebra that were held in the summer of 2016: “Recent Advances in Commutative Ring and Module Theory,” Bressanone, Italy; “Conference on Rings and Polynomials” Graz, Austria. There is also a small collection of invited articles authored by experts in the area who could not attend either of the conferences. Following the model of the talks given at these conferences, the volume contains a number of comprehensive survey papers along with related research articles featuring recent results that have not yet been published elsewhere.

Author : John Dauns
Publisher : Cambridge University Press
Page : 470 pages
File Size : 48,8 Mb
Release : 1994-10-28
Category : Mathematics
ISBN : 9780521462587

Get Book

Modules and Rings by John Dauns Pdf

This book on modern module and non-commutative ring theory is ideal for beginning graduate students. It starts at the foundations of the subject and progresses rapidly through the basic concepts to help the reader reach current research frontiers. Students will have the chance to develop proofs, solve problems, and to find interesting questions. The first half of the book is concerned with free, projective, and injective modules, tensor algebras, simple modules and primitive rings, the Jacobson radical, and subdirect products. Later in the book, more advanced topics, such as hereditary rings, categories and functors, flat modules, and purity are introduced. These later chapters will also prove a useful reference for researchers in non-commutative ring theory. Enough background material (including detailed proofs) is supplied to give the student a firm grounding in the subject.

Author : Alberto Facchini
Publisher : Springer Science & Business Media
Page : 296 pages
File Size : 46,9 Mb
Release : 2012-02-03
Category : Mathematics
ISBN : 9783034803038

Get Book

Module Theory by Alberto Facchini Pdf

This book presents topics in module theory and ring theory: some, such as Goldie dimension and semiperfect rings are now considered classical and others more specialized, such as dual Goldie dimension, semilocal endomorphism rings, serial rings and modules.

Author : David Dobbs
Publisher : CRC Press
Page : 578 pages
File Size : 50,9 Mb
Release : 2023-08-25
Category : Mathematics
ISBN : 9781000939637

Get Book

Advances in Commutative Ring Theory by David Dobbs Pdf

"Presents the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco. Details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examines wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry."

Author : Golan
Publisher : CRC Press
Page : 272 pages
File Size : 42,6 Mb
Release : 2017-10-19
Category : Mathematics
ISBN : 9781351430371

Get Book

Modules and the Structure of Rings by Golan Pdf

This textbook is designed for students with at least one solid semester of abstract algebra,some linear algebra background, and no previous knowledge of module theory. Modulesand the Structure of Rings details the use of modules over a ring as a means of consideringthe structure of the ring itself--explaining the mathematics and "inductivereasoning" used in working on ring theory challenges and emphasizing modules insteadof rings.Stressing the inductive aspect of mathematical research underlying the formal deductivestyle of the literature, this volume offers vital background on current methods for solvinghard classification problems of algebraic structures. Written in an informal butcompletely rigorous style, Modules and the Structure of Rings clarifies sophisticatedproofs ... avoids the formalism of category theory ... aids independent study or seminarwork ... and supplies end-of-chapter problems.This book serves as an excellent primary.text for upper-level undergraduate and graduatestudents in one-semester courses on ring or module theory-laying a foundation formore advanced study of homological algebra or module theory.

Author : D. G. Northcott
Publisher : Unknown
Page : 472 pages
File Size : 54,8 Mb
Release : 2008-12-11
Category : Mathematics
ISBN : UOM:39015080846812

Get Book

Lessons on Rings, Modules and Multiplicities by D. G. Northcott Pdf

This volume provides a clear and self-contained introduction to important results in the theory of rings and modules. Assuming only the mathematical background provided by a normal undergraduate curriculum, the theory is derived by comparatively direct and simple methods. It will be useful to both undergraduates and research students specialising in algebra. In his usual lucid style the author introduces the reader to advanced topics in a manner which makes them both interesting and easy to assimilate. As the text gives very full explanations, a number of well-ordered exercises are included at the end of each chapter. These lead on to further significant results and give the reader an opportunity to devise his own arguments and to test his understanding of the subject.

Author : Michiel Hazewinkel,Nadiya M. Gubareni
Publisher : CRC Press
Page : 388 pages
File Size : 45,8 Mb
Release : 2016-04-05
Category : Mathematics
ISBN : 9781482245059

Get Book

Algebras, Rings and Modules by Michiel Hazewinkel,Nadiya M. Gubareni Pdf

The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth century. This volume is a continuation and an in-depth study, stressing the non-commutative nature of the first two volumes of Algebras, Rings and Modules by M. Hazewinkel, N. Gubareni, and V. V. Kirichenko. It is largely independent of the other volumes. The relevant constructions and results from earlier volumes have been presented in this volume.

Author : Alberto Facchini,Evan Houston,Luigi Salce
Publisher : CRC Press
Page : 530 pages
File Size : 53,6 Mb
Release : 2020-02-10
Category : Mathematics
ISBN : 0824750810

Get Book

Rings, Modules, Algebras, and Abelian Groups by Alberto Facchini,Evan Houston,Luigi Salce Pdf

Rings, Modules, Algebras, and Abelian Groups summarizes the proceedings of a recent algebraic conference held at Venice International University in Italy. Surveying the most influential developments in the field, this reference reviews the latest research on Abelian groups, algebras and their representations, module and ring theory, and topological