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 Separable Algebras Over Commutative Rings written by Frank De Meyer and published by . This book was released on 2014-01-15 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Separable Algebras written by Timothy J. Ford and published by American Mathematical Soc.. This book was released on 2017-09-26 with total page 637 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Download or read book The Separable Galois Theory of Commutative Rings Second Edition written by Andy R. Magid and published by CRC Press. This book was released on 2014-07-14 with total page 186 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 new chapter on the theory of separable algebras. The book develops the notion of commutative separable algebra over a given commutative ring and explains how to construct an equivalent category of profinite spaces on which a profinite groupoid acts. It explores how the connection between the categories depends on the construction of a suitable separable closure of the given ring, which in turn depends on certain notions in profinite topology. The book also discusses how to handle rings with infinitely many idempotents using profinite topological spaces and other methods.

Download or read book Locally Strongly Separable Algebras Over Connected Commutative Rings written by John Frederick Yeagley and published by . This book was released on 1972 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Separable Algebras and Free Cubic Extensions Over Commutative Rings written by Stuart Sui-sheng Wang and published by . This book was released on 1975 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Separable Jordan Algebras Over Commutative Rings written by Robert Alan Bix and published by . This book was released on 1979 with total page 40 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Linear Algebra over Commutative Rings written by Bernard R. McDonald and published by CRC Press. This book was released on 2020-11-26 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph arose from lectures at the University of Oklahoma on topics related to linear algebra over commutative rings. It provides an introduction of matrix theory over commutative rings. The monograph discusses the structure theory of a projective module.

Download or read book Lectures on Exterior Algebras Over Commutative Rings written by Robert B. Gardner and published by . This book was released on 1972 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 79 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Some Results on Separability and Pure Inseparability for Algebras Over Commutative Rings written by Linda Lee Deneen and published by . This book was released on 1980 with total page 120 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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 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 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 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 262 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 Advances in Ring Theory written by J L Chen and published by World Scientific. This book was released on 2005-08-22 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: The selected papers in this volume cover all the most important areas of ring theory and module theory such as classical ring theory, representation theory, the theory of quantum groups, the theory of Hopf algebras, the theory of Lie algebras and Abelian group theory. The review articles, written by specialists, provide an excellent overview of the various areas of ring and module theory — ideal for researchers looking for a new or related field of study. Also included are original articles showing the trend of current research. Contents:Constructing Morphic Rings (J-L Chen et al.)Rings Whose Simple Modules Have Some Properties (Y Hirano)On a Left H-Ring with Nakayama Automorphism (J Kado)On Lifting Properties of Modules (Y Kuratomi)A Survey of Morphic Modules and Rings (W K Nicholson)Flat Cover and Cotorsion Envelope Commute (P Rothmaler)From Galois Field Extensions to Galois Comodules (R Wisbauer)Galois Coverings of Selfinjective Algebras by Twisted Repetitive Algebras (K Yamagata)and other papers Readership: Algebraists in particular non-commutative ring theorists. Keywords:Perspective Survey;Diversified;Distinctive (Articles);Current Field;Distinguished Invited Speakers

Download or read book Algebra and Its Applications written by Dinh Van Huynh and published by American Mathematical Soc.. This book was released on 2000 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: Among all areas of mathematics, algebra is one of the best suited to find applications within the frame of our booming technological society. The thirty-eight articles in this volume encompass the proceedings of the International Conference on Algebra and Its Applications (Athens, OH, 1999), which explored the applications and interplay among the disciplines of ring theory, linear algebra, and coding theory. The presentations collected here reflect the dialogue between mathematicians involved in theoretical aspects of algebra and mathematicians involved in solving problems where state-of-the-art research tools may be used and applied. This Contemporary Mathematics series volume communicates the potential for collaboration among those interested in exploring the wealth of applications for abstract algebra in fields such as information and coding. The expository papers would serve well as supplemental reading in graduate seminars.