Commutative Ring Theory

Commutative Ring Theory
Title Commutative Ring Theory PDF eBook
Author Hideyuki Matsumura
Publisher Cambridge University Press
Pages 338
Release 1989-05-25
Genre Mathematics
ISBN 9780521367646

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This book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.

Commutative Ring Theory and Applications

Commutative Ring Theory and Applications
Title Commutative Ring Theory and Applications PDF eBook
Author Marco Fontana
Publisher CRC Press
Pages 524
Release 2017-07-27
Genre Mathematics
ISBN 9780203910627

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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

Commutative Algebra

Commutative Algebra
Title Commutative Algebra PDF eBook
Author David Eisenbud
Publisher Springer Science & Business Media
Pages 784
Release 2013-12-01
Genre Mathematics
ISBN 1461253500

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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.

Advances in Commutative Ring Theory

Advances in Commutative Ring Theory
Title Advances in Commutative Ring Theory PDF eBook
Author David Dobbs
Publisher CRC Press
Pages 578
Release 2023-08-25
Genre Mathematics
ISBN 1000939634

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"Presents the proceedings of the recently held Third International Conference on Commutative Ring Theory in Fez, Morocco. Details the latest developments in commutative algebra and related areas-featuring 26 original research articles and six survey articles on fundamental topics of current interest. Examines wide-ranging developments in commutative algebra, together with connections to algebraic number theory and algebraic geometry."

Algebraic Geometry and Commutative Algebra

Algebraic Geometry and Commutative Algebra
Title Algebraic Geometry and Commutative Algebra PDF eBook
Author Siegfried Bosch
Publisher Springer Nature
Pages 504
Release 2022-04-22
Genre Mathematics
ISBN 1447175239

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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.

Steps in Commutative Algebra

Steps in Commutative Algebra
Title Steps in Commutative Algebra PDF eBook
Author R. Y. Sharp
Publisher Cambridge University Press
Pages 371
Release 2000
Genre Mathematics
ISBN 0521646235

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Introductory account of commutative algebra, aimed at students with a background in basic algebra.

Introduction To Commutative Algebra

Introduction To Commutative Algebra
Title Introduction To Commutative Algebra PDF eBook
Author Michael F. Atiyah
Publisher CRC Press
Pages 140
Release 2018-03-09
Genre Mathematics
ISBN 0429973268

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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.