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Author : Stephen Urban Chase,D. K. Harrison,Alex Rosenberg
Publisher : American Mathematical Soc.
Page : 79 pages
File Size : 46,7 Mb
Release : 1969
Category : Commutative rings
ISBN : 9780821812525
Author : Cornelius Greither
Publisher : Springer
Page : 155 pages
File Size : 54,9 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540475392
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
Page : 184 pages
File Size : 51,7 Mb
Release : 2014-07-14
Category : Mathematics
ISBN : 9781482208061
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
Page : 280 pages
File Size : 45,9 Mb
Release : 2020-08-26
Category : Mathematics
ISBN : 9781000103786
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.
Page : 290 pages
File Size : 51,8 Mb
Release : 1992
Category : Mathematics
ISBN : 0821831402
This collection consists of original work on Galois theory, rings and algebras, algebraic geometry, group representations, algebraic K—theory and some of their applications.
Author : Frank De Meyer,Edward Ingraham
Publisher : Springer
Page : 162 pages
File Size : 54,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540364849
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 : Unknown
Page : 134 pages
File Size : 50,5 Mb
Release : 1974
Category : Algèbre commutative
ISBN : 0824761634
Author : Andy R. Magid
Publisher : CRC Press
Page : 262 pages
File Size : 47,9 Mb
Release : 2020-09-10
Category : Mathematics
ISBN : 9781000116816
"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."
Author : John Rognes
Publisher : American Mathematical Soc.
Page : 154 pages
File Size : 52,6 Mb
Release : 2008
Category : Commutative algebra
ISBN : 9780821840764
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 : D. E. Dobbs
Publisher : Springer
Page : 183 pages
File Size : 48,5 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540363101
Author : Stefaan Caenepeel
Publisher : Springer Science & Business Media
Page : 512 pages
File Size : 54,8 Mb
Release : 1998
Category : Mathematics
ISBN : 079234829X
This volume is devoted to the Brauer group of a commutative ring and related invariants. Part I presents a self-contained exposition of the Brauer group of a commutative ring. Included is a systematic development of the theory of Grothendieck topologies and etale cohomology, and discussion of topics such as Gabber's theorem and the theory of Taylor's big Brauer group of algebras without a unit. Part II presents a systematic development of the Galois theory of Hopf algebras with special emphasis on the group of Galois objects of a cocommutative Hopf algebra.
Author : Michiel Hazewinkel
Publisher : Springer Science & Business Media
Page : 540 pages
File Size : 41,5 Mb
Release : 1988
Category : Mathematics
ISBN : 1556080034
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.
Author : Frank DeMeyer,David Harrison,Rick Miranda
Publisher : American Mathematical Soc.
Page : 73 pages
File Size : 41,5 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821824573
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.
Author : Victor P Snaith
Publisher : World Scientific Publishing Company
Page : 172 pages
File Size : 42,6 Mb
Release : 1998-09-22
Category : Mathematics
ISBN : 9789813105287
This book is ideally suited for a two-term, undergraduate algebra course culminating in Galois theory. It gives an introduction to group theory and to ring theory en route. In addition, the chapter on groups, including applications to error-correcting codes and to solving the Rubik's cube, is suitable for a one-term course. The book's concise style is intended to foster student-instructor discussion, as is the selection of exercises of various levels of difficulty. Request Inspection Copy
Author : Philippe Gille,Tamás Szamuely
Publisher : Cambridge University Press
Page : 26 pages
File Size : 49,9 Mb
Release : 2006-08-10
Category : Mathematics
ISBN : 9781139458726
This book is the first comprehensive, modern introduction to the theory of central simple algebras over arbitrary fields. Starting from the basics, it reaches such advanced results as the Merkurjev-Suslin theorem. This theorem is both the culmination of work initiated by Brauer, Noether, Hasse and Albert and the starting point of current research in motivic cohomology theory by Voevodsky, Suslin, Rost and others. Assuming only a solid background in algebra, but no homological algebra, the book covers the basic theory of central simple algebras, methods of Galois descent and Galois cohomology, Severi-Brauer varieties, residue maps and, finally, Milnor K-theory and K-cohomology. The last chapter rounds off the theory by presenting the results in positive characteristic, including the theorem of Bloch-Gabber-Kato. The book is suitable as a textbook for graduate students and as a reference for researchers working in algebra, algebraic geometry or K-theory.