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 Dissertation Abstracts International written by and published by . This book was released on 1981 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Comprehensive Dissertation Index Mathematics Statistics Physics A E written by and published by . This book was released on 1984 with total page 1008 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Comprehensive Dissertation Index written by and published by . This book was released on 1984 with total page 914 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Commutative Algebra Volume II written by Oscar Zariski and published by Courier Dover Publications. This book was released on 2019-11-13 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: The second text in this two-book series extends the classical material of Volume I, which focuses on field theory and the ideal theory of Noetherian rings and Dedekind domains. The connection of Volume II's material to algebraic geometry is stressed throughout the presentation, making this book a practical introduction to some basic concepts and the arithmetical foundations of algebraic geometry. The opening chapter deals with properties of places and is followed by a chapter that explores the classical properties of polynomial and power series rings and their applications to algebraic geometry. The final chapter examines the theory of local rings, which provides the algebraic basis for the local study of algebraic and analytical varieties. Several helpful Appendixes conclude the text.
Download or read book Mathematical Reviews written by and published by . This book was released on 2006 with total page 828 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Pacific Journal of Mathematics written by and published by . This book was released on 1980 with total page 1140 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Commutative Algebra written by Oscar Zariski and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second volume of our treatise on commutative algebra deals largely with three basic topics, which go beyond the more or less classical material of volume I and are on the whole of a more advanced nature and a more recent vintage. These topics are: (a) valuation theory; (b) theory of polynomial and power series rings (including generalizations to graded rings and modules); (c) local algebra. Because most of these topics have either their source or their best motivation in algebraic geom etry, the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered through out the exposition. Thus, this volume can be used in part as an introduc tion to some basic concepts and the arithmetic foundations of algebraic geometry. The reader who is not immediately concerned with geometric applications may omit the algebro-geometric material in a first reading (see" Instructions to the reader," page vii), but it is only fair to say that many a reader will find it more instructive to find out immediately what is the geometric motivation behind the purely algebraic material of this volume. The first 8 sections of Chapter VI (including § 5bis) deal directly with properties of places, rather than with those of the valuation associated with a place. These, therefore, are properties of valuations in which the value group of the valuation is not involved.
Download or read book Commutative Algebra II written by O. Zariski and published by Springer Science & Business Media. This book was released on 1976-03-29 with total page 433 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the Preface: "topics are: (a) valuation theory; (b) theory of polynomial and power series rings (including generalizations to graded rings and modules); (c) local algebra... the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered throughout the exposition. Thus, this volume can be used in part as an introduction to some basic concepts and the arithmetic foundations of algebraic geometry."
Download or read book Notices of the American Mathematical Society written by American Mathematical Society and published by . This book was released on 1981 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Lecture Notes in Pure and Applied Mathematics written by and published by . This book was released on 1977 with total page 776 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Advanced Algebra written by Anthony W. Knapp and published by Springer Science & Business Media. This book was released on 2007-10-11 with total page 757 pages. Available in PDF, EPUB and Kindle. Book excerpt: Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Advanced Algebra includes chapters on modern algebra which treat various topics in commutative and noncommutative algebra and provide introductions to the theory of associative algebras, homological algebras, algebraic number theory, and algebraic geometry. Many examples and hundreds of problems are included, along with hints or complete solutions for most of the problems. Together the two books give the reader a global view of algebra and its role in mathematics as a whole.
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 Introduction To Commutative Algebra written by Michael F. Atiyah and published by CRC Press. This book was released on 2018-03-09 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.
Download or read book Quaternion Algebras written by John Voight and published by Springer Nature. This book was released on 2021-06-28 with total page 877 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access textbook presents a comprehensive treatment of the arithmetic theory of quaternion algebras and orders, a subject with applications in diverse areas of mathematics. Written to be accessible and approachable to the graduate student reader, this text collects and synthesizes results from across the literature. Numerous pathways offer explorations in many different directions, while the unified treatment makes this book an essential reference for students and researchers alike. Divided into five parts, the book begins with a basic introduction to the noncommutative algebra underlying the theory of quaternion algebras over fields, including the relationship to quadratic forms. An in-depth exploration of the arithmetic of quaternion algebras and orders follows. The third part considers analytic aspects, starting with zeta functions and then passing to an idelic approach, offering a pathway from local to global that includes strong approximation. Applications of unit groups of quaternion orders to hyperbolic geometry and low-dimensional topology follow, relating geometric and topological properties to arithmetic invariants. Arithmetic geometry completes the volume, including quaternionic aspects of modular forms, supersingular elliptic curves, and the moduli of QM abelian surfaces. Quaternion Algebras encompasses a vast wealth of knowledge at the intersection of many fields. Graduate students interested in algebra, geometry, and number theory will appreciate the many avenues and connections to be explored. Instructors will find numerous options for constructing introductory and advanced courses, while researchers will value the all-embracing treatment. Readers are assumed to have some familiarity with algebraic number theory and commutative algebra, as well as the fundamentals of linear algebra, topology, and complex analysis. More advanced topics call upon additional background, as noted, though essential concepts and motivation are recapped throughout.
Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Download or read book Trivial Extensions of Abelian Categories written by R.M. Fossum and published by Springer. This book was released on 2006-11-15 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt:
