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 DeMeyer and published by Springer. This book was released on 1971 with total page 606 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 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 Separable Algebras written by Timothy J. Ford and published by American Mathematical Soc.. This book was released on 2017-09-26 with total page 664 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 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 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 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 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 Advances In Ring Theory Proceedings Of The 4th China japan korea International Conference written by Jianlong Chen and published by World Scientific. This book was released on 2005-08-22 with total page 335 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.
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 Algebra and Its Applications written by Mohammad Ashraf and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-08-06 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume showcases mostly the contributions presented at the International Conference in Algebra and Its Applications held at the Aligarh Muslim University, Aligarh, India during November 12-14, 2016. Refereed by renowned experts in the field, this wide-ranging collection of works presents the state of the art in the field of algebra and its applications covering topics such as derivations in rings, category theory, Baer module theory, coding theory, graph theory, semi-group theory, HNP rings, Leavitt path algebras, generalized matrix algebras, Nakayama conjecture, near ring theory and lattice theory. All of the contributing authors are leading international academicians and researchers in their respective fields. Contents On Structure of ∗-Prime Rings with Generalized Derivation A characterization of additive mappings in rings with involution| Skew constacyclic codes over Fq + vFq + v2Fq Generalized total graphs of commutative rings: A survey Differential conditions for which near-rings are commutative rings Generalized Skew Derivations satisfying the second Posner’s theorem on Lie ideals Generalized Skew-Derivations on Lie Ideals in Prime Rings On generalized derivations and commutativity of prime rings with involution On (n, d)-Krull property in amalgamated algebra Pure ideals in ordered Γ-semigroups Projective ideals of differential polynomial rings over HNP rings Additive central m-power skew-commuting maps on semiprime rings A Note on CESS-Lattices Properties Inherited by Direct Sums of Copies of a Module Modules witnessing that a Leavitt path algebra is directly infinite Inductive Groupoids and Normal Categories of Regular Semigroups Actions of generalized derivations in Rings and Banach Algebras Proper Categories and Their Duals On Nakayama Conjecture and related conjectures-Review On construction of global actions for partial actions On 2-absorbing and Weakly 2-absorbing Ideals in Product Lattices Separability in algebra and category theory Annihilators of power values of generalized skew derivations on Lie ideals Generalized derivations on prime rings with involution
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 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.
Download or read book Canadian Journal of Mathematics written by and published by . This book was released on 1973-08 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book New Examples of Frobenius Extensions written by Lars Kadison and published by American Mathematical Soc.. This book was released on 1999 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is based on the author's lecture courses to algebraists at Munich and at Goteborg. He presents a unified approach from the point of view of Frobenius algebras/extensions. The book is intended for graduate students and research mathematicians working in algebra and topology.
Download or read book Encyclopaedia of Mathematics written by Michiel Hazewinkel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ENCYCLOPAEDIA OF MATHEMATICS aims to be a reference work for all parts of mathe matics. It is a translation with updates and editorial comments of the Soviet Mathematical Encyclopaedia published by 'Soviet Encyclopaedia Publishing House' in five volumes in 1977-1985. The annotated translation consists of ten volumes including a special index volume. There are three kinds of articles in this ENCYCLOPAEDIA. First of all there are survey-type articles dealing with the various main directions in mathematics (where a rather fine subdivi sion has been used). The main requirement for these articles has been that they should give a reasonably complete up-to-date account of the current state of affairs in these areas and that they should be maximally accessible. On the whole, these articles should be understandable to mathematics students in their first specialization years, to graduates from other mathematical areas and, depending on the specific subject, to specialists in other domains of science, en gineers and teachers of mathematics. These articles treat their material at a fairly general level and aim to give an idea of the kind of problems, techniques and concepts involved in the area in question. They also contain background and motivation rather than precise statements of precise theorems with detailed definitions and technical details on how to carry out proofs and constructions. The second kind of article, of medium length, contains more detailed concrete problems, results and techniques.
