Commutative Ring Theory

Author: H. Matsumura
Editor: Cambridge University Press
ISBN: 9780521367646
File Size: 40,69 MB
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This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.

Commutative Ring Theory And Applications

Author: Marco Fontana
Editor: CRC Press
ISBN: 9780203910627
File Size: 33,76 MB
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Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the growing area of commutative algebra. With contributions from nearly 50 internationally renowned researchers, the book emphasizes innovative applications and connections to algebraic number theory, geome

Advances In Commutative Ring Theory

Author: David Dobbs
Editor: CRC Press
ISBN: 9780824771478
File Size: 54,10 MB
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"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."

Commutative Ring Theory

Author: Paul-Jean Cahen
Editor: CRC Press
ISBN: 9780824798154
File Size: 40,75 MB
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Presents the proceedings of the Second International Conference on Commutative Ring Theory in Fes, Morocco. The text details developments in commutative algebra, highlighting the theory of rings and ideals. It explores commutative algebra's connections with and applications to topological algebra and algebraic geometry.

Non Noetherian Commutative Ring Theory

Author: S.T. Chapman
Editor: Springer Science & Business Media
ISBN: 9780792364924
File Size: 25,76 MB
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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.

Topics In Commutative Ring Theory

Author: John J. Watkins
Editor: Princeton University Press
ISBN: 1400828171
File Size: 33,23 MB
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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 Commutative Ring Theory

Author: Surender K. Jain
Editor: Springer
ISBN: 3540467459
File Size: 59,52 MB
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The papers of this volume share as a common goal the structure and classi- fication of noncommutative rings and their modules, and deal with topics of current research including: localization, serial rings, perfect endomorphism rings, quantum groups, Morita contexts, generalizations of injectivitiy, and Cartan matrices.

Commutative Ring Theory

Author: Cahen
Editor: CRC Press
ISBN: 9780824791704
File Size: 21,91 MB
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" Exploring commutative algebra's connections with and applications to topological algebra and algebraic geometry, Commutative Ring Theory covers the spectra of rings chain conditions, dimension theory, and Jaffard rings fiber products group rings, semigroup rings, and graded rings class groups linear groups integer-valued polynomials rings of finite fractions big Cohen-Macaulay modules and much more!"

Advances In Non Commutative Ring Theory

Author: P. J. Fleury
Editor: Springer
ISBN: 3540393714
File Size: 57,10 MB
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Steps In Commutative Algebra

Author: R. Y. Sharp
Editor: Cambridge University Press
ISBN: 9780521646239
File Size: 14,11 MB
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This introductory account of commutative algebra is aimed at advanced undergraduates and first year graduate students. Assuming only basic abstract algebra, it provides a good foundation in commutative ring theory, from which the reader can proceed to more advanced works in commutative algebra and algebraic geometry. The style throughout is rigorous but concrete, with exercises and examples given within chapters, and hints provided for the more challenging problems used in the subsequent development. After reminders about basic material on commutative rings, ideals and modules are extensively discussed, with applications including to canonical forms for square matrices. The core of the book discusses the fundamental theory of commutative Noetherian rings. Affine algebras over fields, dimension theory and regular local rings are also treated, and for this second edition two further chapters, on regular sequences and Cohen–Macaulay rings, have been added. This book is ideal as a route into commutative algebra.

Zero Dimensional Commutative Rings

Author: David F. Anderson
Editor: CRC Press
ISBN: 9780824796051
File Size: 55,56 MB
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This work presents advances in zero-dimensional commutative rings and commutative algebra. It illustrates the research frontier with 52 open problems together with comments on the relevant literature, and offers a comprehensive index for easy access to information. Wide-ranging developments in commutative ring theory are examined.

Finite Commutative Rings And Their Applications

Author: Gilberto Bini
Editor: Springer Science & Business Media
ISBN: 1461509572
File Size: 18,43 MB
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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.

Power Series Over Commutative Rings

Author: Brewer
Editor: CRC Press
ISBN: 9780824769529
File Size: 30,16 MB
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Algebraic Coding Theory Over Finite Commutative Rings

Author: Steven T. Dougherty
Editor: Springer
ISBN: 3319598066
File Size: 68,56 MB
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This book provides a self-contained introduction to algebraic coding theory over finite Frobenius rings. It is the first to offer a comprehensive account on the subject. Coding theory has its origins in the engineering problem of effective electronic communication where the alphabet is generally the binary field. Since its inception, it has grown as a branch of mathematics, and has since been expanded to consider any finite field, and later also Frobenius rings, as its alphabet. This book presents a broad view of the subject as a branch of pure mathematics and relates major results to other fields, including combinatorics, number theory and ring theory. Suitable for graduate students, the book will be of interest to anyone working in the field of coding theory, as well as algebraists and number theorists looking to apply coding theory to their own work.

The Separable Galois Theory Of Commutative Rings Second Edition

Author: Andy R. Magid
Editor: CRC Press
ISBN: 1482208067
File Size: 11,66 MB
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The Separable Galois Theory of Commutative Rings, Second Edition provides a complete and self-contained account of the Galois theory of commutative rings from the viewpoint of categorical classification theorems and using solely the techniques of commutative algebra. Along with updating nearly every result and explanation, this edition contains a new chapter on the theory of separable algebras. The book develops the notion of commutative separable algebra over a given commutative ring and explains how to construct an equivalent category of profinite spaces on which a profinite groupoid acts. It explores how the connection between the categories depends on the construction of a suitable separable closure of the given ring, which in turn depends on certain notions in profinite topology. The book also discusses how to handle rings with infinitely many idempotents using profinite topological spaces and other methods.

Galois Theory And Cohomology Of Commutative Rings

Author: Stephen Urban Chase
Editor: American Mathematical Soc.
ISBN: 0821812521
File Size: 72,67 MB
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Commutative Rings With Zero Divisors

Author: James Huckaba
Editor: CRC Press
ISBN: 9780824778446
File Size: 30,60 MB
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The first book-length discussion to provide a unified treatment of commutative ring theory for rings containing zero divisors by the ideal theoretic method, Commutative Rings with Zero Divisors also examines other important questions regarding the ideals of rings with zero divisors that do not have counterparts for integral domains -- for example, determining when the space of minimal prime ideals of a commutative ring is compact. Unique features of this indispensable reference/text include characterizations of the compactness of Min Spec ... development of the theory of Krull rings with zero divisors ... complete review, for rings with zero divisors, of problems on the integral closure of Noetherian rings, polynomial rings, and the ring R(X) ... theory of overrings of polynomial rings ... positive results on chained rings as homomorphic images of valuation domains ... plus much more. In addition, Commutative Rings with Zero Divisors develops properties of two important constructions for rings with zero divisors, idealization and the A + B construction. It contains a large section of examples and counterexamples as well as an index of main results.

Rings Polynomials And Modules

Author: Marco Fontana
Editor: Springer
ISBN: 3319658743
File Size: 80,38 MB
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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.

Ideal Theoretic Methods In Commutative Algebra

Author: Daniel Anderson
Editor: CRC Press
ISBN: 9780824705534
File Size: 43,15 MB
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Includes current work of 38 renowned contributors that details the diversity of thought in the fields of commutative algebra and multiplicative ideal theory. Summarizes recent findings on classes of going-down domains and the going-down property, emphasizing new characterizations and applications, as well as generalizations for commutative rings with zero divisors.

Noncommutative Rings

Author: I. N. Herstein
Editor: Cambridge University Press
ISBN: 9780883850398
File Size: 56,81 MB
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A cross-section of ideas, techniques and results that give the reader an unparalleled introductory overview of the subject.