Mostly Commutative Algebra
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Author | : Antoine Chambert-Loir |
Publisher | : Springer Nature |
Total Pages | : 466 |
Release | : 2021-04-08 |
Genre | : Mathematics |
ISBN | : 3030615952 |
Download (Mostly) Commutative Algebra Book in PDF, Epub and Kindle
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.
Author | : Gert-Martin Greuel |
Publisher | : Springer Science & Business Media |
Total Pages | : 640 |
Release | : 2002 |
Genre | : Computers |
ISBN | : 9783540428978 |
Download A Singular Introduction to Commutative Algebra Book in PDF, Epub and Kindle
CD-ROM contains: "a version of Singular for various platforms (Unix/Linux, Windows, Macintosh:, including all examples and procedures explained in the book."
Author | : Ernst Kunz |
Publisher | : Birkhauser |
Total Pages | : 262 |
Release | : 1985 |
Genre | : Mathematics |
ISBN | : |
Download Introduction to Commutative Algebra and Algebraic Geometry Book in PDF, Epub and Kindle
Author | : Christopher Francisco |
Publisher | : |
Total Pages | : 361 |
Release | : 2012 |
Genre | : Algebra conmutativa |
ISBN | : 9783110250343 |
Download Progress in commutative algebra Book in PDF, Epub and Kindle
This is the second of two volumes of a state-of-the-art survey article collection which emanates from three commutative algebra sessions at the 2009 Fall Southeastern American Mathematical Society Meeting at Florida Atlantic University. The articles reach into diverse areas of commutative algebra and build a bridge between Noetherian and non-Noetherian commutative algebra. The current trends in two of the most active areas of commutative algebra are presented: non-noetherian rings (factorization, ideal theory, integrality), advances from the homological study of noetherian rings (the local theory, graded situation and its interactions with combinatorics and geometry). This second volume discusses closures, decompositions, and factorization.
Author | : Huishi Li |
Publisher | : World Scientific |
Total Pages | : 198 |
Release | : 2004 |
Genre | : Mathematics |
ISBN | : 9789812389510 |
Download An Introduction to Commutative Algebra Book in PDF, Epub and Kindle
- Contains many examples and problems (with hints) - Provides a good introduction for beginners in algebraic number theory and algebraic geometry
Author | : James Thomson Knight |
Publisher | : Cambridge University Press |
Total Pages | : 141 |
Release | : 1971-10-31 |
Genre | : Mathematics |
ISBN | : 0521081939 |
Download Commutative Algebra Book in PDF, Epub and Kindle
This introduction to commutative algebra gives an account of some general properties of rings and modules, with their applications to number theory and geometry. It assumes only that the reader has completed an undergraduate algebra course. The fresh approach and simplicity of proof enable a large amount of material to be covered; exercises and examples are included throughout the notes.
Author | : Gregor Kemper |
Publisher | : Springer Science & Business Media |
Total Pages | : 248 |
Release | : 2010-12-02 |
Genre | : Mathematics |
ISBN | : 3642035450 |
Download A Course in Commutative Algebra Book in PDF, Epub and Kindle
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.
Author | : Michael F. Atiyah |
Publisher | : CRC Press |
Total Pages | : 140 |
Release | : 2018-03-09 |
Genre | : Mathematics |
ISBN | : 0429973268 |
Download Introduction To Commutative Algebra Book in PDF, Epub and Kindle
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 | : Fanggui Wang |
Publisher | : Springer |
Total Pages | : 714 |
Release | : 2017-01-06 |
Genre | : Mathematics |
ISBN | : 9811033374 |
Download Foundations of Commutative Rings and Their Modules Book in PDF, Epub and Kindle
This book provides an introduction to the basics and recent developments of commutative algebra. A glance at the contents of the first five chapters shows that the topics covered are ones that usually are included in any commutative algebra text. However, the contents of this book differ significantly from most commutative algebra texts: namely, its treatment of the Dedekind–Mertens formula, the (small) finitistic dimension of a ring, Gorenstein rings, valuation overrings and the valuative dimension, and Nagata rings. Going further, Chapter 6 presents w-modules over commutative rings as they can be most commonly used by torsion theory and multiplicative ideal theory. Chapter 7 deals with multiplicative ideal theory over integral domains. Chapter 8 collects various results of the pullbacks, especially Milnor squares and D+M constructions, which are probably the most important example-generating machines. In Chapter 9, coherent rings with finite weak global dimensions are probed, and the local ring of weak global dimension two is elaborated on by combining homological tricks and methods of star operation theory. Chapter 10 is devoted to the Grothendieck group of a commutative ring. In particular, the Bass–Quillen problem is discussed. Finally, Chapter 11 aims to introduce relative homological algebra, especially where the related concepts of integral domains which appear in classical ideal theory are defined and investigated by using the class of Gorenstein projective modules. Each section of the book is followed by a selection of exercises of varying degrees of difficulty. This book will appeal to a wide readership from graduate students to academic researchers who are interested in studying commutative algebra.
Author | : Hans Schoutens |
Publisher | : Springer Science & Business Media |
Total Pages | : 215 |
Release | : 2010-07-31 |
Genre | : Mathematics |
ISBN | : 3642133673 |
Download The Use of Ultraproducts in Commutative Algebra Book in PDF, Epub and Kindle
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.