A Galois Theory For Separable Algebras
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The Separable Galois Theory Of Commutative Rings Second Edition
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Author : Andy R. Magid
language : en
Publisher: CRC Press
Release Date : 2014-07-14
The Separable Galois Theory Of Commutative Rings Second Edition written by Andy R. Magid and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-14 with Mathematics categories.
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.
A Galois Theory For Separable Algebras
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Author : Lindsay Childs
language : en
Publisher:
Release Date : 1966
A Galois Theory For Separable Algebras written by Lindsay Childs and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1966 with Algebra, Abstract categories.
Separable Algebras And Galois Theory
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Author : James B. Lipton
language : en
Publisher:
Release Date : 1979
Separable Algebras And Galois Theory written by James B. Lipton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Galois theory categories.
Separable Algebras Over Commutative Rings
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Author : Frank De Meyer
language : en
Publisher: Springer
Release Date : 2006-11-15
Separable Algebras Over Commutative Rings written by Frank De Meyer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.
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.
Separable Algebras
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Author : Timothy J. Ford
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-09-26
Separable Algebras written by Timothy J. Ford and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-26 with Associative rings categories.
This book presents a comprehensive introduction to the theory of separable algebras over commutative rings. After a thorough introduction to the general theory, the fundamental roles played by separable algebras are explored. For example, Azumaya algebras, the henselization of local rings, and Galois theory are rigorously introduced and treated. Interwoven throughout these applications is the important notion of étale algebras. Essential connections are drawn between the theory of separable algebras and Morita theory, the theory of faithfully flat descent, cohomology, derivations, differentials, reflexive lattices, maximal orders, and class groups. The text is accessible to graduate students who have finished a first course in algebra, and it includes necessary foundational material, useful exercises, and many nontrivial examples.
Galois Theory And Cohomology Of Commutative Rings
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Author : Stephen Urban Chase
language : en
Publisher: American Mathematical Soc.
Release Date : 1969
Galois Theory And Cohomology Of Commutative Rings written by Stephen Urban Chase and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1969 with Commutative rings categories.
The Separable Galois Theory Of Commutative Rings
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Author : Andy R. Magid
language : en
Publisher:
Release Date : 1974
The Separable Galois Theory Of Commutative Rings written by Andy R. Magid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Algèbre commutative categories.
The Separable Galois Theory Of Commutative Rings
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Author : Andy R. Magid
language : en
Publisher:
Release Date : 1974
The Separable Galois Theory Of Commutative Rings written by Andy R. Magid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1974 with Commutative algebra categories.
Galois Theory
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Author : Steven H. Weintraub
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-10-20
Galois Theory written by Steven H. Weintraub 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 2008-10-20 with Mathematics categories.
Galois theory is a mature mathematical subject of particular beauty. Any Galois theory book written nowadays bears a great debt to Emil Artin’s classic text "Galois Theory," and this book is no exception. While Artin’s book pioneered an approach to Galois theory that relies heavily on linear algebra, this book’s author takes the linear algebra emphasis even further. This special approach to the subject together with the clarity of its presentation, as well as the choice of topics covered, has made the first edition of this book a more than worthwhile addition to the literature on Galois Theory. The second edition, with a new chapter on transcendental extensions, will only further serve to make the book appreciated by and approachable to undergraduate and beginning graduate math majors.
Algebra
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Author : Siegfried Bosch
language : en
Publisher: Springer
Release Date : 2018-11-02
Algebra written by Siegfried Bosch and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-02 with Mathematics categories.
The material presented here can be divided into two parts. The first, sometimes referred to as abstract algebra, is concerned with the general theory of algebraic objects such as groups, rings, and fields, hence, with topics that are also basic for a number of other domains in mathematics. The second centers around Galois theory and its applications. Historically, this theory originated from the problem of studying algebraic equations, a problem that, after various unsuccessful attempts to determine solution formulas in higher degrees, found its complete clarification through the brilliant ideas of E. Galois. The study of algebraic equations has served as a motivating terrain for a large part of abstract algebra, and according to this, algebraic equations are visible as a guiding thread throughout the book. To underline this point, an introduction to the history of algebraic equations is included. The entire book is self-contained, up to a few prerequisites from linear algebra. It covers most topics of current algebra courses and is enriched by several optional sections that complement the standard program or, in some cases, provide a first view on nearby areas that are more advanced. Every chapter begins with an introductory section on "Background and Overview," motivating the material that follows and discussing its highlights on an informal level. Furthermore, each section ends with a list of specially adapted exercises, some of them with solution proposals in the appendix. The present English edition is a translation and critical revision of the eighth German edition of the Algebra book by the author. The book appeared for the first time in 1993 and, in later years, was complemented by adding a variety of related topics. At the same time it was modified and polished to keep its contents up to date.