Commutative Algebra And Its Applications
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Author | : David Eisenbud |
Publisher | : Springer Science & Business Media |
Total Pages | : 784 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461253500 |
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.
Author | : Marco Fontana |
Publisher | : Walter de Gruyter |
Total Pages | : 395 |
Release | : 2009-09-04 |
Genre | : Mathematics |
ISBN | : 3110213184 |
This volume contains selected refereed papers based on lectures presented at the ‘Fifth International Fez Conference on Commutative Algebra and Applications’ that was held in Fez, Morocco in June 2008. The volume represents new trends and areas of classical research within the field, with contributions from many different countries. In addition, the volume has as a special focus the research and influence of Alain Bouvier on commutative algebra over the past thirty years.
Author | : K.P.S. Bhaskara Rao |
Publisher | : CRC Press |
Total Pages | : 192 |
Release | : 2002-03-21 |
Genre | : Mathematics |
ISBN | : 0203218876 |
The theory of generalized inverses of real or complex matrices has been expertly developed and documented. But the generalized inverses of matrices over rings have received comprehensive treatment only recently. In this book, the author, who contributed to the research and development of the theory, explains his results. He explores regular element
Author | : David Cox |
Publisher | : Springer Science & Business Media |
Total Pages | : 523 |
Release | : 2013-04-17 |
Genre | : Mathematics |
ISBN | : 1475721811 |
Written at a level appropriate to undergraduates, this book covers such topics as the Hilbert Basis Theorem, the Nullstellensatz, invariant theory, projective geometry, and dimension theory. Contains a new section on Axiom and an update about MAPLE, Mathematica and REDUCE.
Author | : Hans Schoutens |
Publisher | : Springer Science & Business Media |
Total Pages | : 215 |
Release | : 2010-07-31 |
Genre | : Mathematics |
ISBN | : 3642133673 |
Exploring ultraproducts of Noetherian local rings from an algebraic perspective, this volume illustrates the many ways they can be used in commutative algebra. The text includes an introduction to tight closure in characteristic zero, a survey of flatness criteria, and more.
Author | : Siegfried Bosch |
Publisher | : Springer Nature |
Total Pages | : 504 |
Release | : 2022-04-22 |
Genre | : Mathematics |
ISBN | : 1447175239 |
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.
Author | : Balwant Singh |
Publisher | : World Scientific |
Total Pages | : 405 |
Release | : 2011 |
Genre | : Mathematics |
ISBN | : 9814313629 |
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.
Author | : Marco Fontana |
Publisher | : CRC Press |
Total Pages | : 520 |
Release | : 2017-07-27 |
Genre | : Mathematics |
ISBN | : 0203910621 |
Featuring presentations from the Fourth International Conference on Commutative Algebra held in Fez, Morocco, this reference presents trends in the growing area of commutative algebra. With contributions from nearly 50 internationally renowned researchers, the book emphasizes innovative applications and connections to algebraic number theory, geome
Author | : Michael F. Atiyah |
Publisher | : CRC Press |
Total Pages | : 140 |
Release | : 2018-03-09 |
Genre | : Mathematics |
ISBN | : 0429973268 |
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.
Author | : R. Y. Sharp |
Publisher | : Cambridge University Press |
Total Pages | : 371 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0521646235 |
Introductory account of commutative algebra, aimed at students with a background in basic algebra.