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Non-Commutative Valuation Rings and Semi-Hereditary Orders, H. Marubayashi; Haruo Miyamoto; Akira Ueda


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Автор: H. Marubayashi; Haruo Miyamoto; Akira Ueda
Название:  Non-Commutative Valuation Rings and Semi-Hereditary Orders
ISBN: 9789048148530
Издательство: Springer
Классификация: ISBN-10: 9048148537
Обложка/Формат: Paperback
Страницы: 192
Вес: 0.29 кг.
Дата издания: 07.12.2010
Серия: K-Monographs in Mathematics
Язык: English
Размер: 234 x 156 x 11
Основная тема: Mathematics
Ссылка на Издательство: Link
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Поставляется из: Германии
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 Schillings Book Sc], which are nowadays called invariant valuation rings, though invariant valuation rings can be traced back to Hasses 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.

Non-Associative and Non-Commutative Algebra and Operator Theory

Автор: Gueye
Название: Non-Associative and Non-Commutative Algebra and Operator Theory
ISBN: 3319329006 ISBN-13(EAN): 9783319329000
Издательство: Springer
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Цена: 121110.00 T
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Описание: Presenting the collaborations of over thirtyinternational experts in the latest developments in pure andapplied mathematics, this volume serves as an anthology of research with acommon basis in algebra, functional analysis and their applications.Special attention is devoted to non-commutative algebras, non-associativealgebras, operator theory and ring and module theory. These themes arerelevant in research and development in coding theory, cryptography and quantummechanics. The topics in this volume were presented at the Workshop on Non-Associative& Non-Commutative Algebra and Operator Theory, held May23—25, 2014 at Cheikh Anta Diop University in Dakar, Senegal in honorof Professor Amin Kaidi. The workshop was hosted by theuniversity's Laboratory of Algebra,Cryptology, Algebraic Geometry and Applications, in cooperation withthe University of Almer?a and the University of M?laga. Dr.Kaidi's work focuses on non-associative rings and algebras, operator theory andfunctional analysis, and he has served as a mentor to a generation ofmathematicians in Senegal and around the world.

Advances in Non-Commutative Ring Theory

Автор: P. J. Fleury
Название: Advances in Non-Commutative Ring Theory
ISBN: 3540115978 ISBN-13(EAN): 9783540115977
Издательство: Springer
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Цена: 23250.00 T
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Non-commutative Multiple-Valued Logic Algebras

Автор: Lavinia Corina Ciungu
Название: Non-commutative Multiple-Valued Logic Algebras
ISBN: 3319015885 ISBN-13(EAN): 9783319015880
Издательство: Springer
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Цена: 46570.00 T
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Описание: This monograph provides a self-contained introduction to non-commutative multiple-valued logic algebras. It includes treatment of pseudo-BCK algebras, pseudo-hoops, residuated lattices, bounded divisible residuated lattices, and pseudo-MV algebras.

Quantum and Non-Commutative Analysis

Автор: Huzihiro Araki; Keiichi R. Ito; Akitaka Kishimoto;
Название: Quantum and Non-Commutative Analysis
ISBN: 079232532X ISBN-13(EAN): 9780792325321
Издательство: Springer
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Цена: 130610.00 T
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Описание: In the past decade, there has been a sudden and vigorous development in a number of research areas in mathematics and mathematical physics, such as theory of operator algebras, knot theory, theory of manifolds, infinite dimensional Lie algebras and quantum groups (as a new topics), etc.

Non-Commutative Harmonic Analysis and Lie Groups

Автор: Jaques Carmona; Patrick Delorme; Michele Vergne
Название: Non-Commutative Harmonic Analysis and Lie Groups
ISBN: 3540177019 ISBN-13(EAN): 9783540177012
Издательство: Springer
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Цена: 32560.00 T
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Описание: All the papers in this volume are research papers presenting new results. Most of the results concern semi-simple Lie groups and non-Riemannian symmetric spaces: unitarisation, discrete series characters, multiplicities, orbital integrals. Some, however, also apply to related fields such as Dirac operators and characters in the general case.

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.

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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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.

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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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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Finite Commutative Rings and Their Applications

Автор: Gilberto Bini; Flaminio Flamini
Название: Finite Commutative Rings and Their Applications
ISBN: 1461353238 ISBN-13(EAN): 9781461353232
Издательство: Springer
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Цена: 93160.00 T
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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.



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