Download or read book Commutative Algebra written by Oscar Zariski and published by . This book was released on 1975 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Computational Commutative Algebra 1 written by Martin Kreuzer and published by Springer Science & Business Media. This book was released on 2008-07-15 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to polynomial rings, Gröbner bases and applications bridges the gap in the literature between theory and actual computation. It details numerous applications, covering fields as disparate as algebraic geometry and financial markets. To aid in a full understanding of these applications, more than 40 tutorials illustrate how the theory can be used. The book also includes many exercises, both theoretical and practical.
Download or read book Algebras Rings and Modules written by Michiel Hazewinkel and published by CRC Press. This book was released on 2016-04-05 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of algebras, rings, and modules is one of the fundamental domains of modern mathematics. General algebra, more specifically non-commutative algebra, is poised for major advances in the twenty-first century (together with and in interaction with combinatorics), just as topology, analysis, and probability experienced in the twentieth centu
Download or read book Basic Commutative Algebra written by Balwant Singh and published by World Scientific. This book was released on 2011 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook, set for a one or two semester course in commutative algebra, provides an introduction to commutative algebra at the postgraduate and research levels. The main prerequisites are familiarity with groups, rings and fields. Proofs are self-contained. The book will be useful to beginners and experienced researchers alike. The material is so arranged that the beginner can learn through self-study or by attending a course. For the experienced researcher, the book may serve to present new perspectives on some well-known results, or as a reference.
Download or read book Computational Commutative Algebra 2 written by Martin Kreuzer and published by Springer Science & Business Media. This book was released on 2005-07-06 with total page 592 pages. Available in PDF, EPUB and Kindle. Book excerpt: "The second volume of the authors’ ‘Computational commutative algebra’...covers on its 586 pages a wealth of interesting material with several unexpected applications. ... an encyclopedia on computational commutative algebra, a source for lectures on the subject as well as an inspiration for seminars. The text is recommended for all those who want to learn and enjoy an algebraic tool that becomes more and more relevant to different fields of applications." --ZENTRALBLATT MATH
Download or read book Commutative Algebra written by David Eisenbud and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.
Download or read book Undergraduate Commutative Algebra written by Miles Reid and published by Cambridge University Press. This book was released on 1995-11-30 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commutative algebra is at the crossroads of algebra, number theory and algebraic geometry. This textbook is affordable and clearly illustrated, and is intended for advanced undergraduate or beginning graduate students with some previous experience of rings and fields. Alongside standard algebraic notions such as generators of modules and the ascending chain condition, the book develops in detail the geometric view of a commutative ring as the ring of functions on a space. The starting point is the Nullstellensatz, which provides a close link between the geometry of a variety V and the algebra of its coordinate ring A=k[V]; however, many of the geometric ideas arising from varieties apply also to fairly general rings. The final chapter relates the material of the book to more advanced topics in commutative algebra and algebraic geometry. It includes an account of some famous 'pathological' examples of Akizuki and Nagata, and a brief but thought-provoking essay on the changing position of abstract algebra in today's world.
Download or read book Introduction to Commutative Algebra and Algebraic Geometry written by Ernst Kunz and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.
Download or read book Algebraic Geometry and Commutative Algebra written by Siegfried Bosch and published by Springer Nature. This book was released on 2022-04-22 with total page 504 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic Geometry is a fascinating branch of Mathematics that combines methods from both Algebra and Geometry. It transcends the limited scope of pure Algebra by means of geometric construction principles. Putting forward this idea, Grothendieck revolutionized Algebraic Geometry in the late 1950s by inventing schemes. Schemes now also play an important role in Algebraic Number Theory, a field that used to be far away from Geometry. The new point of view paved the way for spectacular progress, such as the proof of Fermat's Last Theorem by Wiles and Taylor. This book explains the scheme-theoretic approach to Algebraic Geometry for non-experts, while more advanced readers can use it to broaden their view on the subject. A separate part presents the necessary prerequisites from Commutative Algebra, thereby providing an accessible and self-contained introduction to advanced Algebraic Geometry. Every chapter of the book is preceded by a motivating introduction with an informal discussion of its contents and background. Typical examples, and an abundance of exercises illustrate each section. Therefore the book is an excellent companion for self-studying or for complementing skills that have already been acquired. It can just as well serve as a convenient source for (reading) course material and, in any case, as supplementary literature. The present edition is a critical revision of the earlier text.
Download or read book Steps in Commutative Algebra written by R. Y. Sharp and published by Cambridge University Press. This book was released on 2000 with total page 371 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introductory account of commutative algebra, aimed at students with a background in basic algebra.
Download or read book Commutative Algebra written by Marco Fontana and published by Springer Science & Business Media. This book was released on 2010-09-29 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: Commutative algebra is a rapidly growing subject that is developing in many different directions. This volume presents several of the most recent results from various areas related to both Noetherian and non-Noetherian commutative algebra. This volume contains a collection of invited survey articles by some of the leading experts in the field. The authors of these chapters have been carefully selected for their important contributions to an area of commutative-algebraic research. Some topics presented in the volume include: generalizations of cyclic modules, zero divisor graphs, class semigroups, forcing algebras, syzygy bundles, tight closure, Gorenstein dimensions, tensor products of algebras over fields, as well as many others. This book is intended for researchers and graduate students interested in studying the many topics related to commutative algebra.
Download or read book Algebra written by B.L. van der Waerden and published by Springer Science & Business Media. This book was released on 2003-10-17 with total page 312 pages. Available in PDF, EPUB and Kindle. Book excerpt: This beautiful text transformed the graduate teaching of algebra in Europe and the United States. It clearly and succinctly formulated the conceptual and structural insights which Noether had expressed so forcefully and combined it with the elegance and understanding with which Artin had lectured. This second volume of the English translation of B.L. van der Waerden’s text Algebra is the first softcover printing of the original translation.
Download or read book Computational Methods in Commutative Algebra and Algebraic Geometry written by Wolmer Vasconcelos and published by Springer Science & Business Media. This book was released on 2004-05-18 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ACM volume deals with tackling problems that can be represented by data structures which are essentially matrices with polynomial entries, mediated by the disciplines of commutative algebra and algebraic geometry. The discoveries stem from an interdisciplinary branch of research which has been growing steadily over the past decade. The author covers a wide range, from showing how to obtain deep heuristics in a computation of a ring, a module or a morphism, to developing means of solving nonlinear systems of equations - highlighting the use of advanced techniques to bring down the cost of computation. Although intended for advanced students and researchers with interests both in algebra and computation, many parts may be read by anyone with a basic abstract algebra course.
Download or read book A Course in Commutative Algebra written by Gregor Kemper and published by Springer Science & Business Media. This book was released on 2010-12-02 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook offers a thorough, modern introduction into commutative algebra. It is intented mainly to serve as a guide for a course of one or two semesters, or for self-study. The carefully selected subject matter concentrates on the concepts and results at the center of the field. The book maintains a constant view on the natural geometric context, enabling the reader to gain a deeper understanding of the material. Although it emphasizes theory, three chapters are devoted to computational aspects. Many illustrative examples and exercises enrich the text.
Download or read book Mostly Commutative Algebra written by Antoine Chambert-Loir and published by Springer Nature. This book was released on 2021-04-08 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book stems from lectures on commutative algebra for 4th-year university students at two French universities (Paris and Rennes). At that level, students have already followed a basic course in linear algebra and are essentially fluent with the language of vector spaces over fields. The topics introduced include arithmetic of rings, modules, especially principal ideal rings and the classification of modules over such rings, Galois theory, as well as an introduction to more advanced topics such as homological algebra, tensor products, and algebraic concepts involved in algebraic geometry. More than 300 exercises will allow the reader to deepen his understanding of the subject. The book also includes 11 historical vignettes about mathematicians who contributed to commutative algebra.
Download or read book Commutative Ring Theory written by Hideyuki Matsumura and published by Cambridge University Press. This book was released on 1989-05-25 with total page 338 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
