Cyclic Galois Extensions Of Commutative Rings
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Cyclic Galois Extensions Of Commutative Rings
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Author : Cornelius Greither
language : en
Publisher: Springer
Release Date : 2006-11-15
Cyclic Galois Extensions Of Commutative Rings written by Cornelius Greither 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.
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.
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: 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
Galois Extensions Of Structured Ring Spectra Stably Dualizable Groups
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Author : John Rognes
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Galois Extensions Of Structured Ring Spectra Stably Dualizable Groups written by John Rognes 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 2008 with Mathematics categories.
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 $E$.
Quadratic Forms Over Q And Galois Extensions Of Commutative Rings
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Author : Frank DeMeyer
language : en
Publisher:
Release Date : 1989
Quadratic Forms Over Q And Galois Extensions Of Commutative Rings written by Frank DeMeyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Commutative rings categories.
Separable Algebras And Free Cubic Extensions Over Commutative Rings
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Author : Stuart Sui-sheng Wang
language : en
Publisher:
Release Date : 1975
Separable Algebras And Free Cubic Extensions Over Commutative Rings written by Stuart Sui-sheng Wang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975 with Commutative rings categories.
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.
Taming Wild Extensions Hopf Algebras And Local Galois Module Theory
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Author : Lindsay Childs
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Taming Wild Extensions Hopf Algebras And Local Galois Module Theory written by Lindsay Childs 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 2000 with Mathematics categories.
This book studies Hopf algebras over valuation rings of local fields and their application to the theory of wildly ramified extensions of local fields. The results, not previously published in book form, show that Hopf algebras play a natural role in local Galois module theory. Included in this work are expositions of short exact sequences of Hopf algebras; Hopf Galois structures on separable field extensions; a generalization of Noether's theorem on the Galois module structure of tamely ramified extensions of local fields to wild extensions acted on by Hopf algebras; connections between tameness and being Galois for algebras acted on by a Hopf algebra; constructions by Larson and Greither of Hopf orders over valuation rings; ramification criteria of Byott and Greither for the associated order of the valuation ring of an extension of local fields to be Hopf order; the Galois module structure of wildly ramified cyclic extensions of local fields of degree p and p2; and Kummer theory of formal groups. Beyond a general background in graduate-level algebra, some chapters assume an acquaintance with some algebraic number theory. From there, this exposition serves as an excellent resource and motivation for further work in the field.
Rings Extensions And Cohomology
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Author : Andy R. Magid
language : en
Publisher: CRC Press
Release Date : 2020-09-10
Rings Extensions And Cohomology 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 2020-09-10 with Mathematics categories.
"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."
Number Theory
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Author : Jean-Marie De Koninck
language : en
Publisher: Walter de Gruyter
Release Date : 1989
Number Theory written by Jean-Marie De Koninck and has been published by Walter de Gruyter this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with Mathematics categories.
Monumental proceedings (very handsomely produced) of a major international conference. The book contains 74 refereed articles which, apart from a few survey papers of peculiar interest, are mostly research papers (63 in English, 11 in French). The topics covered reflect the full diversity of the current trends and activities in modern number theory: elementary, algebraic and analytic number theory; constructive (computational) number theory; elliptic curves and modular forms; arithmetical geometry; transcendence; quadratic forms; coding theory. (NW) Annotation copyrighted by Book News, Inc., Portland, OR