Topics In Commutative Ring Theory

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Commutative Ring Theory

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Author : Hideyuki Matsumura
language : en
Publisher: Cambridge University Press
Release Date : 1989-05-25

Commutative Ring Theory written by Hideyuki Matsumura and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989-05-25 with Mathematics categories.

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

Topics In Commutative Ring Theory

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Author : John J. Watkins
language : en
Publisher: Princeton University Press
Release Date : 2009-02-09

Topics In Commutative Ring Theory written by John J. Watkins and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-02-09 with Mathematics categories.

Topics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra. Commutative ring theory arose more than a century ago to address questions in geometry and number theory. A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients--with two operations, addition and multiplication. Starting from this simple definition, John Watkins guides readers from basic concepts to Noetherian rings-one of the most important classes of commutative rings--and beyond to the frontiers of current research in the field. Each chapter includes problems that encourage active reading--routine exercises as well as problems that build technical skills and reinforce new concepts. The final chapter is devoted to new computational techniques now available through computers. Careful to avoid intimidating theorems and proofs whenever possible, Watkins emphasizes the historical roots of the subject, like the role of commutative rings in Fermat's last theorem. He leads readers into unexpected territory with discussions on rings of continuous functions and the set-theoretic foundations of mathematics. Written by an award-winning teacher, this is the first introductory textbook to require no prior knowledge of ring theory to get started. Refreshingly informal without ever sacrificing mathematical rigor, Topics in Commutative Ring Theory is an ideal resource for anyone seeking entry into this stimulating field of study.

Non Noetherian Commutative Ring Theory

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Author : S.T. Chapman
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-10-31

Non Noetherian Commutative Ring Theory written by S.T. Chapman 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 2000-10-31 with Mathematics categories.

This volume consists of twenty-one articles by many of the most prominent researchers in non-Noetherian commutative ring theory. The articles combine in various degrees surveys of past results, recent results that have never before seen print, open problems, and an extensive bibliography. One hundred open problems supplied by the authors have been collected in the volume's concluding chapter. The entire collection provides a comprehensive survey of the development of the field over the last ten years and points to future directions of research in the area. Audience: Researchers and graduate students; the volume is an appropriate source of material for several semester-long graduate-level seminars and courses.

Foundations Of Commutative Rings And Their Modules

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Author : Fanggui Wang
language : en
Publisher: Springer
Release Date : 2017-01-06

Foundations Of Commutative Rings And Their Modules written by Fanggui Wang and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-01-06 with Mathematics categories.

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.

Topics In Ring Theory

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Author : I. N. Herstein
language : en
Publisher:
Release Date : 1969

Topics In Ring Theory written by I. N. Herstein and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Mathematics categories.

Topics In The Homological Theory Of Modules Over Commutative Rings

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Author : Melvin Hochster
language : en
Publisher: American Mathematical Soc.
Release Date : 1975

Topics In The Homological Theory Of Modules Over Commutative Rings written by Melvin Hochster 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 1975 with Mathematics categories.

Contains expository lectures from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. This book deals mainly with developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings.

Finite Commutative Rings And Their Applications

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Author : Gilberto Bini
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Finite Commutative Rings And Their Applications written by Gilberto Bini 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 2012-12-06 with Technology & Engineering categories.

Foreword by Dieter Jungnickel Finite Commutative Rings and their Applications answers a need for an introductory reference in finite commutative ring theory as applied to information and communication theory. This book will be of interest to both professional and academic researchers in the fields of communication and coding theory. The book is a concrete and self-contained introduction to finite commutative local rings, focusing in particular on Galois and Quasi-Galois rings. The reader is provided with an active and concrete approach to the study of the purely algebraic structure and properties of finite commutative rings (in particular, Galois rings) as well as to their applications to coding theory. Finite Commutative Rings and their Applications is the first to address both theoretical and practical aspects of finite ring theory. The authors provide a practical approach to finite rings through explanatory examples, thereby avoiding an abstract presentation of the subject. The section on Quasi-Galois rings presents new and unpublished results as well. The authors then introduce some applications of finite rings, in particular Galois rings, to coding theory, using a solid algebraic and geometric theoretical background.

Modules And Rings

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Author : John Dauns
language : en
Publisher: Cambridge University Press
Release Date : 1994-10-28

Modules And Rings written by John Dauns and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-28 with Mathematics categories.

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.

Steps In Commutative Algebra

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Author : R. Y. Sharp
language : en
Publisher: Cambridge University Press
Release Date : 2000

Steps In Commutative Algebra written by R. Y. Sharp and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

Introductory account of commutative algebra, aimed at students with a background in basic algebra.

Theory Of Generalized Inverses Over Commutative Rings

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Author : K.P.S. Bhaskara Rao
language : en
Publisher: CRC Press
Release Date : 2002-03-21

Theory Of Generalized Inverses Over Commutative Rings written by K.P.S. Bhaskara Rao and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-03-21 with Mathematics categories.

The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. The subject of generalized inverses of matrices over rings has now reached a state suitable for a comprehensive treatment - this book provides just that, for mathematicians, algebraists and control theorists.