Download or read book Galois Theory and Cohomology of Commutative Rings written by Stephen Urban Chase and published by American Mathematical Soc.. This book was released on 1969 with total page 87 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Cyclic Galois Extensions of Commutative Rings written by Cornelius Greither and published by Springer. This book was released on 2006-11-15 with total page 155 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book The Separable Galois Theory of Commutative Rings written by Andy R. Magid and published by CRC Press. This book was released on 2014-07-14 with total page 184 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Brauer Groups and the Cohomology of Graded Rings written by Stefaan Caenepeel and published by CRC Press. This book was released on 2020-08-26 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Galois Extensions of Structured Ring Spectra Stably Dualizable Groups written by John Rognes and published by American Mathematical Soc.. This book was released on 2008 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 $E$.
Download or read book Galois Theory Rings Algebraic Groups and Their Applications written by Simeon Ivanov and published by American Mathematical Soc.. This book was released on 1992 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This collection consists of original work on Galois theory, rings and algebras, algebraic geometry, group representations, algebraic K—theory and some of their applications.
Download or read book Rings Hopf Algebras and Brauer Groups written by Stefaan Caenepeel and published by CRC Press. This book was released on 2020-09-30 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: "Based on papers presented at a recent international conference on algebra and algebraic geometry held jointly in Antwerp and Brussels, Belgium. Presents both survey and research articles featuring new results from the intersection of algebra and geometry. "
Download or read book Separable Algebras over Commutative Rings written by Frank De Meyer and published by Springer. This book was released on 2006-11-15 with total page 162 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Rings Extensions and Cohomology written by Andy R. Magid and published by CRC Press. This book was released on 2020-09-10 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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."
Download or read book The Separable Galois Theory of Commutative Rings written by Andy R. Magid and published by . This book was released on 1974 with total page 134 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 1988 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Cech Cohomological Dimensions for Commutative Rings written by D. E. Dobbs and published by Springer. This book was released on 2006-11-15 with total page 183 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Brauer Groups Hopf Algebras and Galois Theory written by Stefaan Caenepeel and published by Springer Science & Business Media. This book was released on 1998 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Quadratic Forms Over Q and Galois Extensions of Commutative Rings written by Frank DeMeyer and published by American Mathematical Soc.. This book was released on 1989 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Groups Rings and Galois Theory written by Victor P Snaith and published by World Scientific Publishing Company. This book was released on 1998-09-22 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Galois Theories written by Francis Borceux and published by Cambridge University Press. This book was released on 2001-02-22 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops Galois theory in a more general context, emphasizing category theory.
Download or read book Central Simple Algebras and Galois Cohomology written by Philippe Gille and published by Cambridge University Press. This book was released on 2006-08-10 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
