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Finite Commutative Rings and Their Applications, Gilberto Bini; Flaminio Flamini


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Автор: Gilberto Bini; Flaminio Flamini
Название:  Finite Commutative Rings and Their Applications
ISBN: 9781461353232
Издательство: Springer
Классификация: ISBN-10: 1461353238
Обложка/Формат: Paperback
Страницы: 176
Вес: 0.28 кг.
Дата издания: 26.10.2012
Серия: The Springer International Series in Engineering and Computer Science
Язык: English
Размер: 234 x 156 x 10
Основная тема: Engineering
Ссылка на Издательство: Link
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Поставляется из: Германии
Описание:

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 The section on Quasi-Galois rings presents new and unpublished results as well.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

This text is suitable for courses in commutative algebra, finite commutative algebra, and coding theory. It is also suitable as a supplementary text for courses in discrete mathematics, finite fields, finite rings, etc.



Non-Commutative Valuation Rings and Semi-Hereditary Orders

Автор: H. Marubayashi; Haruo Miyamoto; Akira Ueda
Название: Non-Commutative Valuation Rings and Semi-Hereditary Orders
ISBN: 9048148537 ISBN-13(EAN): 9789048148530
Издательство: Springer
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Цена: 125730.00 T
Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Much progress has been made during the last decade on the subjects of non- commutative valuation rings, and of semi-hereditary and Priifer orders in a simple Artinian ring which are considered, in a sense, as global theories of non-commu- tative valuation rings. So it is worth to present a survey of the subjects in a self-contained way, which is the purpose of this book. Historically non-commutative valuation rings of division rings were first treat- ed systematically in Schilling's Book Sc], which are nowadays called invariant valuation rings, though invariant valuation rings can be traced back to Hasse's work in Has]. Since then, various attempts have been made to study the ideal theory of orders in finite dimensional algebras over fields and to describe the Brauer groups of fields by usage of "valuations," "places," "preplaces," "value functions" and "pseudoplaces." In 1984, N. 1. Dubrovin defined non-commutative valuation rings of simple Artinian rings with notion of places in the category of simple Artinian rings and obtained significant results on non-commutative valuation rings (named Dubrovin valuation rings after him) which signify that these rings may be the correct def- inition of valuation rings of simple Artinian rings. Dubrovin valuation rings of central simple algebras over fields are, however, not necessarily to be integral over their centers.

Cech Cohomological Dimensions for Commutative Rings

Автор: D. E. Dobbs
Название: Cech Cohomological Dimensions for Commutative Rings
ISBN: 3540049363 ISBN-13(EAN): 9783540049364
Издательство: Springer
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Цена: 23250.00 T
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Combinatorial Aspects of Commutative Algebra and Algebraic Geometry

Автор: Gunnar Fl?ystad; Trygve Johnsen; Andreas Leopold K
Название: Combinatorial Aspects of Commutative Algebra and Algebraic Geometry
ISBN: 3642268285 ISBN-13(EAN): 9783642268281
Издательство: Springer
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Цена: 153720.00 T
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Описание: The Abel Symposium 2009 "Combinatorial aspects of Commutative Algebra and Algebraic Geometry", held at Voss, Norway, featured talks by leading researchers in the field. This is the proceedings of the Symposium, presenting contributions on syzygies, tropical geometry, Boij-Soederberg theory, Schubert calculus, and quiver varieties.

Separable Algebras over Commutative Rings

Автор: Frank De Meyer; Edward Ingraham
Название: Separable Algebras over Commutative Rings
ISBN: 3540053719 ISBN-13(EAN): 9783540053712
Издательство: Springer
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Цена: 23250.00 T
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Non-Commutative Valuation Rings and Semi-Hereditary Orders

Автор: H. Marubayashi; Haruo Miyamoto; Akira Ueda
Название: Non-Commutative Valuation Rings and Semi-Hereditary Orders
ISBN: 0792345622 ISBN-13(EAN): 9780792345626
Издательство: Springer
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Цена: 125730.00 T
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Описание: A summary of non-Noetherian orders in a simple Artinian ring. This book covers Dubrovin valuation rings and semi-hereditary orders, including Prufer and semi-local Bezout orders, which are considered, in a sense, as global theories of Dubrovin valuation rings.

Commutative Rings whose Finitely Generated Modules Decompose

Автор: W. Brandal
Название: Commutative Rings whose Finitely Generated Modules Decompose
ISBN: 3540095071 ISBN-13(EAN): 9783540095071
Издательство: Springer
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Цена: 23250.00 T
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Commutative Coherent Rings

Автор: Sarah Glaz
Название: Commutative Coherent Rings
ISBN: 3540511156 ISBN-13(EAN): 9783540511151
Издательство: Springer
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Цена: 37220.00 T
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Описание: Offers a systematic treatment of the theory of commutative coherent rings. Starting with elementary results, this book advances to topics such as: uniform coherence, regular rings, rings of small homological dimensions, polynomial and power series rings, group rings and symmetric algebra over coherent rings.

Cyclic Galois Extensions of Commutative Rings

Автор: Cornelius Greither
Название: Cyclic Galois Extensions of Commutative Rings
ISBN: 3540563504 ISBN-13(EAN): 9783540563501
Издательство: Springer
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Цена: 23250.00 T
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Описание: This exposition is aimed at readers with some background in either commutative algebra or algebraic number theory. Emphasis is placed on the notion of a normal basis, which allows researchers to view Leopoldt`s conjecture on number theory from a new angle.

Non-Commutative Harmonic Analysis

Автор: J. Carmona; J. Dixmier; M. Vergne
Название: Non-Commutative Harmonic Analysis
ISBN: 3540071830 ISBN-13(EAN): 9783540071839
Издательство: Springer
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Цена: 32560.00 T
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Prime Spectra in Non-Commutative Algebra

Автор: F. van Oystaeyen
Название: Prime Spectra in Non-Commutative Algebra
ISBN: 3540071466 ISBN-13(EAN): 9783540071464
Издательство: Springer
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Цена: 23280.00 T
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Essays in Commutative Harmonic Analysis

Автор: C. C. Graham; O. C. McGehee
Название: Essays in Commutative Harmonic Analysis
ISBN: 1461299780 ISBN-13(EAN): 9781461299783
Издательство: Springer
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Цена: 81050.00 T
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Описание: This book considers various spaces and algebras made up of functions, measures, and other objects-situated always on one or another locally compact abelian group, and studied in the light of the Fourier transform.

Commutative Harmonic Analysis IV

Автор: J. Peetre; V.P. Khavin; Sh.A. Alimov; N.K. Nikol`s
Название: Commutative Harmonic Analysis IV
ISBN: 3642081037 ISBN-13(EAN): 9783642081033
Издательство: Springer
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Цена: 130430.00 T
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Описание: With the groundwork laid in the first volume (EMS 15) of the Commutative Harmonic Analysis subseries of the Encyclopaedia, the present volume takes up four advanced topics in the subject: Littlewood-Paley theory for singular integrals, exceptional sets, multiple Fourier series and multiple Fourier integrals.


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