Commutative Algebra
Author : Oscar Zariski
Publisher :
Page : 0 pages
File Size : 13,44 MB
Release : 1975
Category :
ISBN :
Computational Commutative Algebra 2
Author : Martin Kreuzer
Publisher : Springer Science & Business Media
Page : 592 pages
File Size : 19,12 MB
Release : 2005-07-06
Category : Mathematics
ISBN : 3540255273
Book Description
"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
Computational Commutative Algebra 1
Author : Martin Kreuzer
Publisher : Springer Science & Business Media
Page : 325 pages
File Size : 28,35 MB
Release : 2008-07-15
Category : Mathematics
ISBN : 354067733X
Book Description
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.
Introduction To Commutative Algebra
Author : Michael F. Atiyah
Publisher : CRC Press
Page : 140 pages
File Size : 32,43 MB
Release : 2018-03-09
Category : Mathematics
ISBN : 0429973268
Book Description
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.
Algebra II
Author : Alexey L. Gorodentsev
Publisher : Springer
Page : 377 pages
File Size : 23,13 MB
Release : 2017-02-12
Category : Mathematics
ISBN : 3319508539
Book Description
This book is the second volume of an intensive “Russian-style” two-year undergraduate course in abstract algebra, and introduces readers to the basic algebraic structures – fields, rings, modules, algebras, groups, and categories – and explains the main principles of and methods for working with them. The course covers substantial areas of advanced combinatorics, geometry, linear and multilinear algebra, representation theory, category theory, commutative algebra, Galois theory, and algebraic geometry – topics that are often overlooked in standard undergraduate courses. This textbook is based on courses the author has conducted at the Independent University of Moscow and at the Faculty of Mathematics in the Higher School of Economics. The main content is complemented by a wealth of exercises for class discussion, some of which include comments and hints, as well as problems for independent study.
Undergraduate Commutative Algebra
Author : Miles Reid
Publisher : Cambridge University Press
Page : 172 pages
File Size : 10,12 MB
Release : 1995-11-30
Category : Mathematics
ISBN : 9780521458894
Book Description
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.
Commutative Algebra
Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 784 pages
File Size : 27,8 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461253500
Book Description
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.
Algebra II
Author : N. Bourbaki
Publisher : Springer Science & Business Media
Page : 457 pages
File Size : 42,58 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 3642616984
Book Description
This is a softcover reprint of chapters four through seven of the 1990 English translation of the revised and expanded version of Bourbaki’s Algebre. Much material was added or revised for this edition, which thoroughly establishes the theories of commutative fields and modules over a principal ideal domain.
Basic Commutative Algebra
Author : Balwant Singh
Publisher : World Scientific
Page : 405 pages
File Size : 11,10 MB
Release : 2011
Category : Mathematics
ISBN : 9814313629
Book Description
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.
(Mostly) Commutative Algebra
Author : Antoine Chambert-Loir
Publisher : Springer Nature
Page : 466 pages
File Size : 46,32 MB
Release : 2021-04-08
Category : Mathematics
ISBN : 3030615952
Book Description
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.
