Galois Theory and Cohomology of Commutative Rings PDF Download
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Author: Stephen Urban Chase
Publisher: American Mathematical Soc.
ISBN: 0821812521
Category : Commutative rings
Languages : en
Pages : 79
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Book Description
Author: Stephen Urban Chase
Publisher: American Mathematical Soc.
ISBN: 0821812521
Category : Commutative rings
Languages : en
Pages : 79
Get Book
Book Description
Author: Stephen Urban Chase
Publisher:
ISBN:
Category :
Languages : en
Pages : 19
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Book Description
Author: S. U. Chase
Publisher: American Mathematical Society(RI)
ISBN: 9780821812525
Category :
Languages : en
Pages : 79
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Book Description
Author: Cornelius Greither
Publisher: Springer
ISBN: 3540475397
Category : Mathematics
Languages : en
Pages : 155
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Book Description
The structure theory of abelian extensions of commutative rings is a subjectwhere commutative algebra and algebraic number theory overlap. This exposition is aimed at readers with some background in either of these two fields. Emphasis is given to the notion of a normal basis, which allows one to view in a well-known conjecture in number theory (Leopoldt's conjecture) from a new angle. Methods to construct certain extensions quite explicitly are also described at length.
Author: Andy R. Magid
Publisher: CRC Press
ISBN: 1482208067
Category : Mathematics
Languages : en
Pages : 184
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Book Description
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
Author: Stefaan Caenepeel
Publisher: CRC Press
ISBN: 1000103781
Category : Mathematics
Languages : en
Pages : 280
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Book Description
This book introduces various notions defined in graded terms extending the notions most frequently used as basic ingredients in the theory of Azumaya algebras: separability and Galois extensions of commutative rings, crossed products and Galois cohomology, Picard groups, and the Brauer group.
Author: Simeon Ivanov
Publisher: American Mathematical Soc.
ISBN: 9780821831403
Category : Mathematics
Languages : en
Pages : 290
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Book Description
This collection consists of original work on Galois theory, rings and algebras, algebraic geometry, group representations, algebraic Kâtheory and some of their applications.
Author: John Rognes
Publisher: American Mathematical Soc.
ISBN: 0821840762
Category : Commutative algebra
Languages : en
Pages : 154
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Book Description
The author introduces the notion of a Galois extension of commutative $S$-algebras ($E_\infty$ ring spectra), often localized with respect to a fixed homology theory. There are numerous examples, including some involving Eilenberg-Mac Lane spectra of commutative rings, real and complex topological $K$-theory, Lubin-Tate spectra and cochain $S$-algebras. He establishes the main theorem of Galois theory in this generality. Its proof involves the notions of separable and etale extensions of commutative $S$-algebras, and the Goerss-Hopkins-Miller theory for $E_\infty$ mapping spaces. He shows that the global sphere spectrum $S$ is separably closed, using Minkowski's discriminant theorem, and he estimates the separable closure of its localization with respect to each of the Morava $K$-theories. He also defines Hopf-Galois extensions of commutative $S$-algebras and studies the complex cobordism spectrum $MU$ as a common integral model for all of the local Lubin-Tate Galois extensions. The author extends the duality theory for topological groups from the classical theory for compact Lie groups, via the topological study by J. R. Klein and the $p$-complete study for $p$-compact groups by T. Bauer, to a general duality theory for stably dualizable groups in the $E$-local stable homotopy category, for any spectrum $E$.
Author: Frank De Meyer
Publisher: Springer
ISBN: 3540364846
Category : Mathematics
Languages : en
Pages : 162
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Book Description
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.
Author: Andy R. Magid
Publisher: CRC Press
ISBN: 1000116816
Category : Mathematics
Languages : en
Pages :
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Book Description
"Presenting the proceedings of a conference held recently at Northwestern University, Evanston, Illinois, on the occasion of the retirement of noted mathematician Daniel Zelinsky, this novel reference provides up-to-date coverage of topics in commutative and noncommutative ring extensions, especially those involving issues of separability, Galois theory, and cohomology."
