Rings And Ideals

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Rings and Ideals

Author : Neal H. McCoy
Publisher : American Mathematical Soc.
ISBN 13 : 1614440085
Total Pages : 229 pages
Book Rating : 4.6/5 (144 download)

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Book Synopsis Rings and Ideals by : Neal H. McCoy

Download or read book Rings and Ideals written by Neal H. McCoy and published by American Mathematical Soc.. This book was released on 1948-12-31 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents an introduction to that branch of abstract algebra having to do with the theory of rings, with some emphasis on the role of ideals in the theory. Except for a knowledge of certain fundamental theorems about determinants which is assumed in Chapter VIII, and at one point in Chapter VII, the book is almost entirely self-contained. Of course, the reader must have a certain amount of “mathematical maturity” in order to understand the illustrative examples and also to grasp the significance of the abstract approach. However, as far as formal technique is concerned, little more than the elements of algebra are presupposed.

Integral Closure of Ideals, Rings, and Modules

Author : Craig Huneke
Publisher : Cambridge University Press
ISBN 13 : 0521688604
Total Pages : 446 pages
Book Rating : 4.5/5 (216 download)

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Book Synopsis Integral Closure of Ideals, Rings, and Modules by : Craig Huneke

Download or read book Integral Closure of Ideals, Rings, and Modules written by Craig Huneke and published by Cambridge University Press. This book was released on 2006-10-12 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

A First Course in Rings and Ideals

Author : David M. Burton
Publisher : Addison-Wesley
ISBN 13 :
Total Pages : 328 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis A First Course in Rings and Ideals by : David M. Burton

Download or read book A First Course in Rings and Ideals written by David M. Burton and published by Addison-Wesley. This book was released on 1970 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt:

The Theory of Rings

Author : Nathan Jacobson
Publisher : American Mathematical Soc.
ISBN 13 : 0821815024
Total Pages : 160 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Theory of Rings by : Nathan Jacobson

Download or read book The Theory of Rings written by Nathan Jacobson and published by American Mathematical Soc.. This book was released on 1943-12-31 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is mainly concerned with the theory of rings in which both maximal and minimal conditions hold for ideals (except in the last chapter, where rings of the type of a maximal order in an algebra are considered). The central idea consists of representing rings as rings of endomorphisms of an additive group, which can be achieved by means of the regular representation.

Near Rings, Fuzzy Ideals, and Graph Theory

Author : Bhavanari Satyanarayana
Publisher : CRC Press
ISBN 13 : 1439873100
Total Pages : 482 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Near Rings, Fuzzy Ideals, and Graph Theory by : Bhavanari Satyanarayana

Download or read book Near Rings, Fuzzy Ideals, and Graph Theory written by Bhavanari Satyanarayana and published by CRC Press. This book was released on 2013-05-21 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Near Rings, Fuzzy Ideals, and Graph Theory explores the relationship between near rings and fuzzy sets and between near rings and graph theory. It covers topics from recent literature along with several characterizations. After introducing all of the necessary fundamentals of algebraic systems, the book presents the essentials of near rings theory, relevant examples, notations, and simple theorems. It then describes the prime ideal concept in near rings, takes a rigorous approach to the dimension theory of N-groups, gives some detailed proofs of matrix near rings, and discusses the gamma near ring, which is a generalization of both gamma rings and near rings. The authors also provide an introduction to fuzzy algebraic systems, particularly the fuzzy ideals of near rings and gamma near rings. The final chapter explains important concepts in graph theory, including directed hypercubes, dimension, prime graphs, and graphs with respect to ideals in near rings. Near ring theory has many applications in areas as diverse as digital computing, sequential mechanics, automata theory, graph theory, and combinatorics. Suitable for researchers and graduate students, this book provides readers with an understanding of near ring theory and its connection to fuzzy ideals and graph theory.

Exercises in Basic Ring Theory

Author : Grigore Calugareanu
Publisher : Springer Science & Business Media
ISBN 13 : 9780792349181
Total Pages : 226 pages
Book Rating : 4.3/5 (491 download)

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Book Synopsis Exercises in Basic Ring Theory by : Grigore Calugareanu

Download or read book Exercises in Basic Ring Theory written by Grigore Calugareanu and published by Springer Science & Business Media. This book was released on 1998-02-28 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each undergraduate course of algebra begins with basic notions and results concerning groups, rings, modules and linear algebra. That is, it begins with simple notions and simple results. Our intention was to provide a collection of exercises which cover only the easy part of ring theory, what we have named the "Basics of Ring Theory". This seems to be the part each student or beginner in ring theory (or even algebra) should know - but surely trying to solve as many of these exercises as possible independently. As difficult (or impossible) as this may seem, we have made every effort to avoid modules, lattices and field extensions in this collection and to remain in the ring area as much as possible. A brief look at the bibliography obviously shows that we don't claim much originality (one could name this the folklore of ring theory) for the statements of the exercises we have chosen (but this was a difficult task: indeed, the 28 titles contain approximatively 15.000 problems and our collection contains only 346). The real value of our book is the part which contains all the solutions of these exercises. We have tried to draw up these solutions as detailed as possible, so that each beginner can progress without skilled help. The book is divided in two parts each consisting of seventeen chapters, the first part containing the exercises and the second part the solutions.

Rings and Their Modules

Author : Paul E. Bland
Publisher : Walter de Gruyter
ISBN 13 : 3110250225
Total Pages : 467 pages
Book Rating : 4.1/5 (12 download)

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Book Synopsis Rings and Their Modules by : Paul E. Bland

Download or read book Rings and Their Modules written by Paul E. Bland and published by Walter de Gruyter. This book was released on 2011 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of rings and modules that goes beyond what one normally obtains in a graduate course in abstract algebra. In addition to the presentation of standard topics in ring and module theory, it also covers category theory, homological algebra and even more specialized topics like injective envelopes and proj

Determinantal Rings

Author : Winfried Bruns
Publisher : Springer
ISBN 13 : 3540392742
Total Pages : 246 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Determinantal Rings by : Winfried Bruns

Download or read book Determinantal Rings written by Winfried Bruns and published by Springer. This book was released on 2006-11-14 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Determinantal rings and varieties have been a central topic of commutative algebra and algebraic geometry. Their study has attracted many prominent researchers and has motivated the creation of theories which may now be considered part of general commutative ring theory. The book gives a first coherent treatment of the structure of determinantal rings. The main approach is via the theory of algebras with straightening law. This approach suggest (and is simplified by) the simultaneous treatment of the Schubert subvarieties of Grassmannian. Other methods have not been neglected, however. Principal radical systems are discussed in detail, and one section is devoted to each of invariant and representation theory. While the book is primarily a research monograph, it serves also as a reference source and the reader requires only the basics of commutative algebra together with some supplementary material found in the appendix. The text may be useful for seminars following a course in commutative ring theory since a vast number of notions, results, and techniques can be illustrated significantly by applying them to determinantal rings.

Foundations of Module and Ring Theory

Author : Robert Wisbauer
Publisher : Routledge
ISBN 13 : 1351447343
Total Pages : 622 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Foundations of Module and Ring Theory by : Robert Wisbauer

Download or read book Foundations of Module and Ring Theory written by Robert Wisbauer and published by Routledge. This book was released on 2018-05-11 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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. It is a useful and stimulating study for those new to the subject as well as for researchers and serves as a reference volume. Starting form a basic understanding of linear algebra, the theory is presented and accompanied by complete proofs. For a module M, the smallest Grothendieck category containing it is denoted by o[M] and module theory is developed in this category. Developing the techniques in o[M] is no more complicated than in full module categories and the higher generality yields significant advantages: for example, module theory may be developed for rings without units and also for non-associative rings. Numerous exercises are included in this volume to give further insight into the topics covered and to draw attention to related results in the literature.

The Theory of Rings

Author : Neal H. MacCoy
Publisher :
ISBN 13 :
Total Pages : 161 pages
Book Rating : 4.:/5 (174 download)

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Book Synopsis The Theory of Rings by : Neal H. MacCoy

Download or read book The Theory of Rings written by Neal H. MacCoy and published by . This book was released on 1973 with total page 161 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebra: Chapter 0

Author : Paolo Aluffi
Publisher : American Mathematical Soc.
ISBN 13 : 147046571X
Total Pages : 713 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Algebra: Chapter 0 by : Paolo Aluffi

Download or read book Algebra: Chapter 0 written by Paolo Aluffi and published by American Mathematical Soc.. This book was released on 2021-11-09 with total page 713 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra: Chapter 0 is a self-contained introduction to the main topics of algebra, suitable for a first sequence on the subject at the beginning graduate or upper undergraduate level. The primary distinguishing feature of the book, compared to standard textbooks in algebra, is the early introduction of categories, used as a unifying theme in the presentation of the main topics. A second feature consists of an emphasis on homological algebra: basic notions on complexes are presented as soon as modules have been introduced, and an extensive last chapter on homological algebra can form the basis for a follow-up introductory course on the subject. Approximately 1,000 exercises both provide adequate practice to consolidate the understanding of the main body of the text and offer the opportunity to explore many other topics, including applications to number theory and algebraic geometry. This will allow instructors to adapt the textbook to their specific choice of topics and provide the independent reader with a richer exposure to algebra. Many exercises include substantial hints, and navigation of the topics is facilitated by an extensive index and by hundreds of cross-references.

Commutative Algebra

Author : Melvin Hochster
Publisher : Springer Science & Business Media
ISBN 13 : 1461236606
Total Pages : 516 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Commutative Algebra by : Melvin Hochster

Download or read book Commutative Algebra written by Melvin Hochster and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: During late June and early July of 1987 a three week program (dubbed "microprogram") in Commutative Algebra was held at the Mathematical Sciences Research Institute at Berkeley. The intent of the microprogram was to survey recent major results and current trends in the theory of commutative rings, especially commutative Noetherian rings. There was enthusiastic international participation. The papers in this volume, some of which are expository, some strictly research, and some a combination, reflect the intent of the program. They give a cross-section of what is happening now in this area. Nearly all of the manuscripts were solicited from the speakers at the conference, and in most instances the manuscript is based on the conference lecture. The editors hope that they will be of interest and of use both to experts and neophytes in the field. The editors would like to express their appreciation to the director of MSRI, Professor Irving Kaplansky, who first suggested the possibility of such a conference and made the task of organization painless. We would also like to thank the IVISRI staff who were unfailingly efficient, pleasant, and helpful during the meeting, and the manager of MSRI, Arlene Baxter, for her help with this volume. Finally we would like to express our appreciation to David Mostardi who did much of the typing and put the electronic pieces together.

A First Course in Abstract Algebra

Author : Marlow Anderson
Publisher : CRC Press
ISBN 13 : 1420057111
Total Pages : 684 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis A First Course in Abstract Algebra by : Marlow Anderson

Download or read book A First Course in Abstract Algebra written by Marlow Anderson and published by CRC Press. This book was released on 2005-01-27 with total page 684 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most abstract algebra texts begin with groups, then proceed to rings and fields. While groups are the logically simplest of the structures, the motivation for studying groups can be somewhat lost on students approaching abstract algebra for the first time. To engage and motivate them, starting with something students know and abstracting from there

Commutative Ring Theory

Author : Hideyuki Matsumura
Publisher : Cambridge University Press
ISBN 13 : 9780521367646
Total Pages : 338 pages
Book Rating : 4.3/5 (676 download)

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Book Synopsis Commutative Ring Theory by : Hideyuki Matsumura

Download or read book Commutative Ring Theory written by Hideyuki Matsumura and published by Cambridge University Press. This book was released on 1989-05-25 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.

Introduction To Commutative Algebra

Author : Michael F. Atiyah
Publisher : CRC Press
ISBN 13 : 0429973268
Total Pages : 140 pages
Book Rating : 4.4/5 (299 download)

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Book Synopsis Introduction To Commutative Algebra by : Michael F. Atiyah

Download or read book Introduction To Commutative Algebra written by Michael F. Atiyah and published by CRC Press. This book was released on 2018-03-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.

Multiplicative Theory of Ideals

Author :
Publisher : Academic Press
ISBN 13 : 0080873561
Total Pages : 317 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Multiplicative Theory of Ideals by :

Download or read book Multiplicative Theory of Ideals written by and published by Academic Press. This book was released on 1971-10-11 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Multiplicative Theory of Ideals

Rings and Categories of Modules

Author : Frank W. Anderson
Publisher : Springer Science & Business Media
ISBN 13 : 1461244188
Total Pages : 386 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Rings and Categories of Modules by : Frank W. Anderson

Download or read book Rings and Categories of Modules written by Frank W. Anderson and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.