The Separable Galois Theory Of Commutative Rings

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The Separable Galois Theory Of Commutative Rings

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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 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 n

The Separable Galois Theory Of Commutative Rings

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Author : Andy Roy Magid
language : en
Publisher:
Release Date : 1974

The Separable Galois Theory Of Commutative Rings written by Andy Roy 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.

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 Connections And Applications

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Author : K. Denecke
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11

Galois Connections And Applications written by K. Denecke 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 2013-11-11 with Mathematics categories.

Galois connections provide the order- or structure-preserving passage between two worlds of our imagination - and thus are inherent in hu man thinking wherever logical or mathematical reasoning about cer tain hierarchical structures is involved. Order-theoretically, a Galois connection is given simply by two opposite order-inverting (or order preserving) maps whose composition yields two closure operations (or one closure and one kernel operation in the order-preserving case). Thus, the "hierarchies" in the two opposite worlds are reversed or transported when passing to the other world, and going forth and back becomes a stationary process when iterated. The advantage of such an "adjoint situation" is that information about objects and relationships in one of the two worlds may be used to gain new information about the other world, and vice versa. In classical Galois theory, for instance, properties of permutation groups are used to study field extensions. Or, in algebraic geometry, a good knowledge of polynomial rings gives insight into the structure of curves, surfaces and other algebraic vari eties, and conversely. Moreover, restriction to the "Galois-closed" or "Galois-open" objects (the fixed points of the composite maps) leads to a precise "duality between two maximal subworlds".

The Separable Galois Theory Of Commutative Rings 2nd Edition

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Author : Andy Magid
language : en
Publisher:
Release Date : 2014

The Separable Galois Theory Of Commutative Rings 2nd Edition written by Andy Magid and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with 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 n.

Encyclopaedia Of Mathematics

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Author : Michiel Hazewinkel
language : en
Publisher: Springer Science & Business Media
Release Date : 1989-08-31

Encyclopaedia Of Mathematics written by Michiel Hazewinkel 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 1989-08-31 with Mathematics categories.

V.1. A-B v.2. C v.3. D-Feynman Measure. v.4. Fibonaccimethod H v.5. Lituus v.6. Lobachevskii Criterion (for Convergence)-Optical Sigman-Algebra. v.7. Orbi t-Rayleigh Equation. v.8. Reaction-Diffusion Equation-Stirling Interpolation Fo rmula. v.9. Stochastic Approximation-Zygmund Class of Functions. v.10. Subject Index-Author Index.

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.

Quadratic Forms Over Q And Galois Extensions Of Commutative Rings

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Author : Frank DeMeyer
language : en
Publisher: American Mathematical Soc.
Release Date : 1989

Quadratic Forms Over Q And Galois Extensions Of Commutative Rings written by Frank DeMeyer 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 1989 with Mathematics categories.

The object of the first two sections of this memoir is to give explicit descriptions of both the Witt ring of the rational numbers [bold]Q and the set of abelian extensions of [bold]Q. The third presents a discussion around a particular case of the Galois cubic extension, building on the general theory.

Galois Theories

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Author : Francis Borceux
language : en
Publisher: Cambridge University Press
Release Date : 2001-02-22

Galois Theories written by Francis Borceux and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-02-22 with Mathematics categories.

Starting from the classical finite-dimensional Galois theory of fields, this book develops Galois theory in a much more general context, presenting work by Grothendieck in terms of separable algebras and then proceeding to the infinite-dimensional case, which requires considering topological Galois groups. In the core of the book, the authors first formalize the categorical context in which a general Galois theorem holds, and then give applications to Galois theory for commutative rings, central extensions of groups, the topological theory of covering maps and a Galois theorem for toposes. The book is designed to be accessible to a wide audience: the prerequisites are first courses in algebra and general topology, together with some familiarity with the categorical notions of limit and adjoint functors. The first chapters are accessible to advanced undergraduates, with later ones at a graduate level. For all algebraists and category theorists this book will be a rewarding read.

Hopf Algebras And Galois Theory

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Author : Stephen U. Chase
language : en
Publisher: Springer
Release Date : 2007-01-05

Hopf Algebras And Galois Theory written by Stephen U. Chase and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-05 with Mathematics categories.