Finite Commutative Rings And Their Applications

Author : Gilberto Bini,Flaminio Flamini
Publisher : Springer Science & Business Media
Page : 181 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461509578

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Finite Commutative Rings and Their Applications by Gilberto Bini,Flaminio Flamini Pdf

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 The section on Quasi-Galois rings presents new and unpublished results as well.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.

Author : Gilberto Bini,Flaminio Flamini
Publisher : Unknown
Page : 192 pages
File Size : 50,9 Mb
Release : 2002-04-30
Category : Electronic
ISBN : 1461509580

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Finite Commutative Rings and Their Applications by Gilberto Bini,Flaminio Flamini Pdf

Author : Fanggui Wang,Hwankoo Kim
Publisher : Springer
Page : 699 pages
File Size : 44,7 Mb
Release : 2017-01-06
Category : Mathematics
ISBN : 9789811033377

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Foundations of Commutative Rings and Their Modules by Fanggui Wang,Hwankoo Kim Pdf

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.

Author : Marco Fontana,Salah-Eddine Kabbaj,Sylvia Wiegand
Publisher : CRC Press
Page : 520 pages
File Size : 44,9 Mb
Release : 2017-07-27
Category : Mathematics
ISBN : 9780203910627

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Commutative Ring Theory and Applications by Marco Fontana,Salah-Eddine Kabbaj,Sylvia Wiegand Pdf

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

Author : Steven Dougherty,Alberto Facchini,Andre Gerard Leroy,Edmund Puczylowski,Patrick Sole
Publisher : American Mathematical Soc.
Page : 280 pages
File Size : 55,9 Mb
Release : 2015-02-20
Category : Mathematics
ISBN : 9781470410322

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Noncommutative Rings and Their Applications by Steven Dougherty,Alberto Facchini,Andre Gerard Leroy,Edmund Puczylowski,Patrick Sole Pdf

Contains the Proceedings of an International Conference on Noncommutative Rings and Their Applications, held July 1-4, 2013, at the Universite d'Artois, Lens, France. It presents recent developments in the theories of noncommutative rings and modules over such rings as well as applications of these to coding theory, enveloping algebras, and Leavitt path algebras.

Author : Lance W. Small
Publisher : American Mathematical Soc.
Page : 118 pages
File Size : 43,8 Mb
Release : 1987
Category : Mathematics
ISBN : 9780821815250

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Noetherian Rings and Their Applications by Lance W. Small Pdf

Researchers in ring theory or allied topics, such as the representation theory of finite dimensional Lie algebras, will appreciate this collection of expository lectures on advances in ring theory and their applications to other areas. Five of the lectures were delivered at a conference on Noetherian rings at the Mathematisches Forschungsinstitut, Oberwolfach, in January 1983, and the sixth was delivered at a London Mathematical Society Durham conference in July 1983. The study of the prime and primitive ideal spectra of various classes of rings forms a common theme in the lectures, and they touch on such topics as the structure of group rings of polycyclic-by-finite groups, localization in non commutative rings, and rings of differential operators. The lectures require the background of an advanced graduate student in ring theory and may be used in seminars in ring theory at this level.

Author : Steven T. Dougherty
Publisher : Springer
Page : 103 pages
File Size : 48,7 Mb
Release : 2017-07-04
Category : Mathematics
ISBN : 9783319598062

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Algebraic Coding Theory Over Finite Commutative Rings by Steven T. Dougherty Pdf

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.

Author : Taylor & Francis Group
Publisher : Unknown
Page : 128 pages
File Size : 52,7 Mb
Release : 2018-10-06
Category : Electronic
ISBN : 1138098515

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Finite Commutative Rings and Their Polynomial Rings by Taylor & Francis Group Pdf

Author : International Conference on Finite Fields and Applications
Publisher : American Mathematical Soc.
Page : 278 pages
File Size : 47,6 Mb
Release : 2008
Category : Coding theory
ISBN : 9780821843093

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Finite Fields and Applications by International Conference on Finite Fields and Applications Pdf

This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007. It contains 5 invited survey papers as well as original research articles covering various theoretical and applied areas related to finite fields.Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas. In particular, finite fields now play very important roles in number theory, algebra, and algebraic geometry, as well as in computer science, statistics, and engineering. Areas of application include algebraic coding theory, cryptology, and combinatorialdesign theory.

Author : I. N. Herstein
Publisher : American Mathematical Soc.
Page : 202 pages
File Size : 52,7 Mb
Release : 1994-12-31
Category : Mathematics
ISBN : 9780883850152

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Noncommutative Rings by I. N. Herstein Pdf

Noncommutative Rings provides a cross-section of ideas, techniques, and results that give the reader an idea of that part of algebra which concerns itself with noncommutative rings. In the space of 200 pages, Herstein covers the Jacobson radical, semisimple rings, commutativity theorems, simple algebras, representations of finite groups, polynomial identities, Goldie's theorem, and the Golod–Shafarevitch theorem. Almost every practicing ring theorist has studied portions of this classic monograph.

Author : Melvin Hochster
Publisher : American Mathematical Soc.
Page : 88 pages
File Size : 54,7 Mb
Release : 1975-12-31
Category : Mathematics
ISBN : 0821888714

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Topics in the Homological Theory of Modules Over Commutative Rings by Melvin Hochster Pdf

This volume contains expository lectures by Melvin Hochster from the CBMS Regional Conference in Mathematics held at the University of Nebraska, June 1974. The lectures deal mainly with recent developments and still open questions in the homological theory of modules over commutative (usually, Noetherian) rings. A good deal of attention is given to the role ``big'' Cohen-Macaulay modules play in clearing up some of the open questions. A modest knowledge of commutative rings and familarity with (the long exact sequences for) Tor and Ext should suffice as a background for the reader.

Author : Stephen Urban Chase,D. K. Harrison,Alex Rosenberg
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 40,6 Mb
Release : 1969
Category : Commutative rings
ISBN : 9780821812525

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Galois Theory and Cohomology of Commutative Rings by Stephen Urban Chase,D. K. Harrison,Alex Rosenberg Pdf

Author : T.Chalapathi,R.V.M.S.S.Kiran Kumar
Publisher : Infinite Study
Page : 10 pages
File Size : 47,9 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 8210379456XXX

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Self Additive Inverse Elements of Neutrosophic Rings and Fields by T.Chalapathi,R.V.M.S.S.Kiran Kumar Pdf

Algebraic Neutrosophic theory is an abstract branch of modern mathematics that originated from classical algebra through the composition of Neutrosophic theory. Its development started few years ago, and now a days Neutrosophic analytic methods and results are important in various fields of engineering science and applied mathematics with its applications.

Author : Frank De Meyer,Edward Ingraham
Publisher : Springer
Page : 162 pages
File Size : 45,6 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540364849

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Separable Algebras over Commutative Rings by Frank De Meyer,Edward Ingraham Pdf

These lecture notes were prepared by the authors for use in graduate courses and seminars, based on the work of many earlier mathematicians. In addition to very elementary results, presented for the convenience of the reader, Chapter I contains the Morita theorems and the definition of the projective class group of a commutative ring. Chapter II addresses the Brauer group of a commutative ring, and automorphisms of separable algebras. Chapter III surveys the principal theorems of the Galois theory for commutative rings. In Chapter IV the authors present a direct derivation of the first six terms of the seven-term exact sequence for Galois cohomology. In the fifth and final chapter the authors illustrate the preceding material with applications to the structure of central simple algebras and the Brauer group of a Dedekind domain, and they pose problems for further investigation. Exercises are included at the end of each chapter.

Author : James Thomson Knight
Publisher : Cambridge University Press
Page : 141 pages
File Size : 49,9 Mb
Release : 1971-10-31
Category : Mathematics
ISBN : 9780521081931

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Commutative Algebra by James Thomson Knight Pdf

This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and examples are included throughout the notes.