Extensions of Rings and Modules

Author: Gary F. Birkenmeier,Jae Keol Park,S Tariq Rizvi

Publisher: Springer Science & Business Media

ISBN: 0387927166

Category: Mathematics

Page: 432

View: 5144

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.
Posted in Mathematics

Ring Theory

Nonsingular Rings and Modules

Author: Kenneth Goodearl

Publisher: CRC Press

ISBN: 9780824763541

Category: Mathematics

Page: 224

View: 9018

Posted in Mathematics

Fields and Rings

Author: Irving Kaplansky

Publisher: University of Chicago Press

ISBN: 9780226424514

Category: Mathematics

Page: 206

View: 3278

This book combines in one volume Irving Kaplansky's lecture notes on the theory of fields, ring theory, and homological dimensions of rings and modules. "In all three parts of this book the author lives up to his reputation as a first-rate mathematical stylist. Throughout the work the clarity and precision of the presentation is not only a source of constant pleasure but will enable the neophyte to master the material here presented with dispatch and ease."—A. Rosenberg, Mathematical Reviews
Posted in Mathematics

Rings, Polynomials, and Modules

Author: Marco Fontana,Sophie Frisch,Sarah Glaz,Francesca Tartarone,Paolo Zanardo

Publisher: Springer

ISBN: 3319658743

Category: Mathematics

Page: 375

View: 7636

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.
Posted in Mathematics

Ring and Module Theory

Author: Toma Albu,Gary F. Birkenmeier,Ali Erdogan,Adnan Tercan

Publisher: Springer Science & Business Media

ISBN: 9783034600071

Category: Mathematics

Page: 200

View: 6922

This book is a collection of invited papers and articles, many presented at the 2008 International Conference on Ring and Module Theory. The papers explore the latest in various areas of algebra, including ring theory, module theory and commutative algebra.
Posted in Mathematics

Algebras, Rings and Modules

Author: Michiel Hazewinkel,Nadiya Gubareni,V.V. Kirichenko

Publisher: Springer Science & Business Media

ISBN: 9781402026904

Category: Mathematics

Page: 380

View: 1520

The text of the first volume of the book covers the major topics in ring and module theory and includes both fundamental classical results and more recent developments. The basic tools of investigation are methods from the theory of modules, which allow a very simple and clear approach both to classical and new results. An unusual main feature of this book is the use of the technique of quivers for studying the structure of rings. A considerable part of the first volume of the book is devoted to a study of special classes of rings and algebras, such as serial rings, hereditary rings, semidistributive rings and tiled orders. Many results of this text until now have been available in journal articles only. This book is aimed at graduate and post-graduate students and for all mathematicians who use algebraic techniques in their work. This is a self-contained book which is intended to be a modern textbook on the structure theory of associative rings and algebras and is suitable for independent study.
Posted in Mathematics

Groups, Rings, Modules

Author: Maurice Auslander,David Buchsbaum

Publisher: Courier Corporation

ISBN: 048679542X

Category: Mathematics

Page: 480

View: 9669

Classic monograph covers sets and maps, monoids and groups, unique factorization domains, localization and tensor products, applications of fundamental theorem, algebraic field extension, Dedekind domains, and much more. 1974 edition.
Posted in Mathematics

Advances in Rings and Modules

Author: Sergio R. López-Permouth,Jae Keol Park,S. Tariq Rizvi,Cosmin S. Roman

Publisher: American Mathematical Soc.

ISBN: 1470435551

Category: Modules (Algebra)

Page: 283

View: 4907

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.
Posted in Modules (Algebra)

A Course in Ring Theory

Author: Donald S. Passman

Publisher: American Mathematical Soc.

ISBN: 9780821869383

Category:

Page: 306

View: 7545

Projective modules: Modules and homomorphisms Projective modules Completely reducible modules Wedderburn rings Artinian rings Hereditary rings Dedekind domains Projective dimension Tensor products Local rings Polynomial rings: Skew polynomial rings Grothendieck groups Graded rings and modules Induced modules Syzygy theorem Patching theorem Serre conjecture Big projectives Generic flatness Nullstellensatz Injective modules: Injective modules Injective dimension Essential extensions Maximal ring of quotients Classical ring of quotients Goldie rings Uniform dimension Uniform injective modules Reduced rank Index
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Introduction to the Theory of Topological Rings and Modules

Author: V. Arnautov,S. Glavatsky,Aleksandr Vasilʹevich Mikhalev

Publisher: Courier Corporation

ISBN: 9780824793234

Category: Mathematics

Page: 502

View: 8885

This invaluable reference/text provides a thorough introduction to the theory of topological rings and modules - presenting basic information and focusing on problems of topologization and extensions of ring topologies.
Posted in Mathematics

Das Total Von Moduln und Ringen

Author: Wolfgang Schneider

Publisher: N.A

ISBN: 9783889270368

Category: Modules (Algebra)

Page: 59

View: 3682

Posted in Modules (Algebra)

Commutative Ring Theory

Author: H. Matsumura

Publisher: Cambridge University Press

ISBN: 9780521367646

Category: Mathematics

Page: 320

View: 8879

This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Posted in Mathematics

Integral Closure of Ideals, Rings, and Modules

Author: Craig Huneke,Irena Swanson

Publisher: Cambridge University Press

ISBN: 0521688604

Category: Mathematics

Page: 431

View: 5642

Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.
Posted in Mathematics

Foundations of Module and Ring Theory

Author: Robert Wisbauer

Publisher: CRC Press

ISBN: 9782881248054

Category: Mathematics

Page: 606

View: 756

Translated (with the addition of a number of new results, exercises, and references) from the German original of 1988 (Verlag Reinhard Fischer, Munich), this volume provides a comprehensive introduction to module theory and the related part of ring theory, including original results as well as the most recent work. Starting from a basic understanding of linear algebra, the theory is presented with complete proofs. For undergraduate, graduate, and research level mathematicians working in algebra, module, and ring theory. Annotation copyrighted by Book News, Inc., Portland, OR
Posted in Mathematics

Foundations of Commutative Rings and Their Modules

Author: Fanggui Wang,Hwankoo Kim

Publisher: Springer

ISBN: 9811033374

Category: Mathematics

Page: 699

View: 5021

This book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text. However, the contents of this book differ significantly from most commutative algebra texts: namely, its treatment of the Dedekind–Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings and the valuative dimension, and Nagata rings. Going further, Chapter 6 presents w-modules over commutative rings as they can be most commonly used by torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of the pullbacks, especially Milnor squares and D+M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings with finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated on by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass–Quillen problem is discussed. Finally, Chapter 11 aims to introduce relative homological algebra, especially where the related concepts of integral domains which appear in classical ideal theory are defined and investigated by using the class of Gorenstein projective modules. Each section of the book is followed by a selection of exercises of varying degrees of difficulty. This book will appeal to a wide readership from graduate students to academic researchers who are interested in studying commutative algebra.
Posted in Mathematics

Rings, Extensions, and Cohomology

Author: Andy R. Magid

Publisher: CRC Press

ISBN: 9780824792411

Category: Mathematics

Page: 264

View: 459

"Presenting the proceedings of a conference held recently at Northwestern University, Evanston, Illinois, on the occasion of the retirement of noted mathematician Daniel Zelinsky, this novel reference provides up-to-date coverage of topics in commutative and noncommutative ring extensions, especially those involving issues of separability, Galois theory, and cohomology."
Posted in Mathematics

Rings with Morita Duality

Author: Weimin Xue

Publisher: Springer

ISBN: 3540472835

Category: Mathematics

Page: 170

View: 2260

Associative rings that possess Morita dualities or self- dualities form the object of this book. They are assumed to have an identity and modules are assumed unitary. The book sets out to give an extensive introduction to thisclass of rings, covering artinian rings, ring extensions, Azuma- ya's exact rings, and more. Among the interesting results presented are a characterization of duality via linear com- pactness, ring extensions with dualities, and exact rings. Some basic knowledge of rings and modules is expected of the reader.
Posted in Mathematics

Abstract Algebra with Applications

Volume 2: Rings and Fields

Author: Karlheinz Spindler

Publisher: CRC Press

ISBN: 9780824791599

Category: Mathematics

Page: 552

View: 6694

A comprehensive presentation of abstract algebra and an in-depth treatment of the applications of algebraic techniques and the relationship of algebra to other disciplines, such as number theory, combinatorics, geometry, topology, differential equations, and Markov chains.
Posted in Mathematics

Algebra

A Graduate Course

Author: I. Martin Isaacs

Publisher: American Mathematical Soc.

ISBN: 9780821847992

Category: Mathematics

Page: 516

View: 5677

as a student." --Book Jacket.
Posted in Mathematics

Manis Valuations and Prüfer Extensions I

A New Chapter in Commutative Algebra

Author: Manfred Knebusch,Digen Zhang

Publisher: Springer

ISBN: 3540456252

Category: Mathematics

Page: 274

View: 9098

The present book is devoted to a study of relative Prüfer rings and Manis valuations, with an eye to application in real and p-adic geometry. If one wants to expand on the usual algebraic geometry over a non-algebraically closed base field, e.g. a real closed field or p-adically closed field, one typically meets lots of valuation domains. Usually they are not discrete and hence not noetherian. Thus, for a further develomemt of real algebraic and real analytic geometry in particular, and certainly also rigid analytic and p-adic geometry, new chapters of commutative algebra are needed, often of a non-noetherian nature. The present volume presents one such chapter.
Posted in Mathematics