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Author: Hideyuki Matsumura
Publisher: Cambridge University Press
Published: 1989-05-25
Total Pages: 338
ISBN-13: 9780521367646
DOWNLOAD EBOOKThis book explores commutative ring theory, an important a foundation for algebraic geometry and complex analytical geometry.
Author: Marco Fontana
Publisher: CRC Press
Published: 2017-07-27
Total Pages: 524
ISBN-13: 9780203910627
DOWNLOAD EBOOKFeaturing 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: David Dobbs
Publisher: CRC Press
Published: 2023-08-25
Total Pages: 578
ISBN-13: 1000939634
DOWNLOAD EBOOK"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."
Author: David F. Anderson
Publisher: CRC Press
Published: 1995-04-10
Total Pages: 820
ISBN-13: 9780824796051
DOWNLOAD EBOOKThis work presents advances in zero-dimensional commutative rings and commutative algebra. It illustrates the research frontier with 52 open problems together with comments on the relevant literature, and offers a comprehensive index for easy access to information. Wide-ranging developments in commutative ring theory are examined.
Author: David Eisenbud
Publisher: Springer Science & Business Media
Published: 2013-12-01
Total Pages: 784
ISBN-13: 1461253500
DOWNLOAD EBOOKThis 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: R. Y. Sharp
Publisher: Cambridge University Press
Published: 2000
Total Pages: 371
ISBN-13: 0521646235
DOWNLOAD EBOOKIntroductory account of commutative algebra, aimed at students with a background in basic algebra.
Author: Michael F. Atiyah
Publisher: CRC Press
Published: 2018-03-09
Total Pages: 140
ISBN-13: 0429973268
DOWNLOAD EBOOKFirst 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: John J. Watkins
Publisher: Princeton University Press
Published: 2009-02-09
Total Pages: 228
ISBN-13: 1400828171
DOWNLOAD EBOOKTopics in Commutative Ring Theory is a textbook for advanced undergraduate students as well as graduate students and mathematicians seeking an accessible introduction to this fascinating area of abstract algebra. Commutative ring theory arose more than a century ago to address questions in geometry and number theory. A commutative ring is a set-such as the integers, complex numbers, or polynomials with real coefficients--with two operations, addition and multiplication. Starting from this simple definition, John Watkins guides readers from basic concepts to Noetherian rings-one of the most important classes of commutative rings--and beyond to the frontiers of current research in the field. Each chapter includes problems that encourage active reading--routine exercises as well as problems that build technical skills and reinforce new concepts. The final chapter is devoted to new computational techniques now available through computers. Careful to avoid intimidating theorems and proofs whenever possible, Watkins emphasizes the historical roots of the subject, like the role of commutative rings in Fermat's last theorem. He leads readers into unexpected territory with discussions on rings of continuous functions and the set-theoretic foundations of mathematics. Written by an award-winning teacher, this is the first introductory textbook to require no prior knowledge of ring theory to get started. Refreshingly informal without ever sacrificing mathematical rigor, Topics in Commutative Ring Theory is an ideal resource for anyone seeking entry into this stimulating field of study.
Author: Siegfried Bosch
Publisher: Springer Nature
Published: 2022-04-22
Total Pages: 504
ISBN-13: 1447175239
DOWNLOAD EBOOKAlgebraic 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: Paul M. Cohn
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 234
ISBN-13: 1447104757
DOWNLOAD EBOOKA clear and structured introduction to the subject. After a chapter on the definition of rings and modules there are brief accounts of Artinian rings, commutative Noetherian rings and ring constructions, such as the direct product, Tensor product and rings of fractions, followed by a description of free rings. Readers are assumed to have a basic understanding of set theory, group theory and vector spaces. Over two hundred carefully selected exercises are included, most with outline solutions.
