Almost Ring Theory
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Almost Ring Theory
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Author : Ofer Gabber
language : en
Publisher: Springer
Release Date : 2003-12-09
Almost Ring Theory written by Ofer Gabber and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-09 with Mathematics categories.
The authors develop thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an "almost ring". Almost rings are the commutative unitary monoids in a tensor category obtained as a quotient V-Mod/S of the category V-Mod of modules over a fixed ring V; the subcategory S consists of all modules annihilated by a fixed ideal m of V, satisfying certain natural conditions. The reader is assumed to be familiar with general categorical notions, some basic commutative algebra and some advanced homological algebra (derived categories, simplicial methods). Apart from these general prerequisites, the text is as self-contained as possible. One novel feature of the book - compared with Faltings' earlier treatment - is the systematic exploitation of the cotangent complex, especially for the study of deformations of almost algebras.
Almost Ring Theory
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Author : Ofer Gabber
language : en
Publisher:
Release Date : 2014-01-15
Almost Ring Theory written by Ofer Gabber and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.
Almost Ring Theory
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Author : Ofer Gabber
language : en
Publisher: Springer Science & Business Media
Release Date : 2003
Almost Ring Theory written by Ofer Gabber and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Arithmetical algebraic geometry categories.
Almost Ring Theory
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Author : Ofer Gabber
language : en
Publisher: Springer
Release Date : 2003-08-11
Almost Ring Theory written by Ofer Gabber and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-08-11 with Mathematics categories.
The authors develop thorough and complete foundations for the method of almost etale extensions, which is at the basis of Faltings' approach to p-adic Hodge theory. The central notion is that of an "almost ring". Almost rings are the commutative unitary monoids in a tensor category obtained as a quotient V-Mod/S of the category V-Mod of modules over a fixed ring V; the subcategory S consists of all modules annihilated by a fixed ideal m of V, satisfying certain natural conditions. The reader is assumed to be familiar with general categorical notions, some basic commutative algebra and some advanced homological algebra (derived categories, simplicial methods). Apart from these general prerequisites, the text is as self-contained as possible. One novel feature of the book - compared with Faltings' earlier treatment - is the systematic exploitation of the cotangent complex, especially for the study of deformations of almost algebras.
Foundations Of Module And Ring Theory
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Author : Robert Wisbauer
language : en
Publisher: CRC Press
Release Date : 1991-09-05
Foundations Of Module And Ring Theory written by Robert Wisbauer and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-09-05 with Mathematics categories.
Translated (with the addition of a number of new results, exercises, and references) from the German original of 1988 (Verlag Reinhard Fischer, Munich), 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. Starting from a basic understanding of linear algebra, the theory is presented with complete proofs. For undergraduate, graduate, and research level mathematicians working in algebra, module, and ring theory. Annotation copyrighted by Book News, Inc., Portland, OR
Associative Algebras
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Author : R.S. Pierce
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Associative Algebras written by R.S. Pierce and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
For many people there is life after 40; for some mathematicians there is algebra after Galois theory. The objective ofthis book is to prove the latter thesis. It is written primarily for students who have assimilated substantial portions of a standard first year graduate algebra textbook, and who have enjoyed the experience. The material that is presented here should not be fatal if it is swallowed by persons who are not members of that group. The objects of our attention in this book are associative algebras, mostly the ones that are finite dimensional over a field. This subject is ideal for a textbook that will lead graduate students into a specialized field of research. The major theorems on associative algebras inc1ude some of the most splendid results of the great heros of algebra: Wedderbum, Artin, Noether, Hasse, Brauer, Albert, Jacobson, and many others. The process of refine ment and c1arification has brought the proof of the gems in this subject to a level that can be appreciated by students with only modest background. The subject is almost unique in the wide range of contacts that it makes with other parts of mathematics. The study of associative algebras con tributes to and draws from such topics as group theory, commutative ring theory, field theory, algebraic number theory, algebraic geometry, homo logical algebra, and category theory. It even has some ties with parts of applied mathematics.
Rings Related To Stable Range Conditions
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Author : Huanyin Chen
language : en
Publisher: World Scientific
Release Date : 2011-01-26
Rings Related To Stable Range Conditions written by Huanyin Chen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-26 with Mathematics categories.
This monograph is concerned with exchange rings in various conditions related to stable range. Diagonal reduction of regular matrices and cleanness of square matrices are also discussed. Readers will come across various topics: cancellation of modules, comparability of modules, cleanness, monoid theory, matrix theory, K-theory, topology, amongst others. This is a first-ever book that contains many of these topics considered under stable range conditions. It will be of great interest to researchers and graduate students involved in ring and module theories.
Homological And Computational Methods In Commutative Algebra
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Author : Aldo Conca
language : en
Publisher: Springer
Release Date : 2017-11-16
Homological And Computational Methods In Commutative Algebra written by Aldo Conca and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-11-16 with Mathematics categories.
This volume collects contributions by leading experts in the area of commutative algebra related to the INdAM meeting “Homological and Computational Methods in Commutative Algebra” held in Cortona (Italy) from May 30 to June 3, 2016 . The conference and this volume are dedicated to Winfried Bruns on the occasion of his 70th birthday. In particular, the topics of this book strongly reflect the variety of Winfried Bruns’ research interests and his great impact on commutative algebra as well as its applications to related fields. The authors discuss recent and relevant developments in algebraic geometry, commutative algebra, computational algebra, discrete geometry and homological algebra. The book offers a unique resource, both for young and more experienced researchers seeking comprehensive overviews and extensive bibliographic references.
Introduction To Ring Theory
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Author : Paul M. Cohn
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Introduction To Ring Theory written by Paul M. Cohn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Most parts of algebra have undergone great changes and advances in recent years, perhaps none more so than ring theory. In this volume, Paul Cohn provides a clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product. Tensor product and rings of fractions, followed by a description of free rings. The reader is assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.
Near Rings The Theory And Its Applications
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Author :
language : en
Publisher: Elsevier
Release Date : 2011-10-10
Near Rings The Theory And Its Applications written by and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-10-10 with Mathematics categories.
Near-rings: The Theory and its Applications