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Introduction to Commutative Algebra and Algebraic Geometry

Author: Ernst Kunz

Publisher: Springer Science & Business Media

Published: 2012-11-06

Total Pages: 253

ISBN-13: 1461459877

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Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.

Book Synopsis Introduction to Commutative Algebra and Algebraic Geometry by : Ernst Kunz

Download or read book Introduction to Commutative Algebra and Algebraic Geometry written by Ernst Kunz and published by Springer Science & Business Media. This book was released on 2012-11-06 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published in 1985, this classic textbook is an English translation of Einführung in die kommutative Algebra und algebraische Geometrie. As part of the Modern Birkhäuser Classics series, the publisher is proud to make Introduction to Commutative Algebra and Algebraic Geometry available to a wider audience. Aimed at students who have taken a basic course in algebra, the goal of the text is to present important results concerning the representation of algebraic varieties as intersections of the least possible number of hypersurfaces and—a closely related problem—with the most economical generation of ideals in Noetherian rings. Along the way, one encounters many basic concepts of commutative algebra and algebraic geometry and proves many facts which can then serve as a basic stock for a deeper study of these subjects.

A Course in Commutative Algebra

Author: Gregor Kemper

Publisher: Springer Science & Business Media

Published: 2010-12-02

Total Pages: 248

ISBN-13: 3642035450

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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.

Book Synopsis A Course in Commutative Algebra by : Gregor Kemper

Download or read book A Course in Commutative Algebra written by Gregor Kemper and published by Springer Science & Business Media. This book was released on 2010-12-02 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction To Commutative Algebra

Author: Michael Atiyah

Publisher: Addison Wesley Publishing Company

Published: 1994-02-21

Total Pages: 140

ISBN-13: 0201407515

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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

Book Synopsis Introduction To Commutative Algebra by : Michael Atiyah

Download or read book Introduction To Commutative Algebra written by Michael Atiyah and published by Addison Wesley Publishing Company. This book was released on 1994-02-21 with total page 140 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

An Introductory Course in Commutative Algebra

Author: A. W. Chatters

Publisher: Clarendon Press

Published: 1998

Total Pages: 156

ISBN-13: 9780198501442

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This introduction to topics in commutative algebra combines algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields.

Book Synopsis An Introductory Course in Commutative Algebra by : A. W. Chatters

Download or read book An Introductory Course in Commutative Algebra written by A. W. Chatters and published by Clarendon Press. This book was released on 1998 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introduction to topics in commutative algebra combines algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields.

Commutative Algebra

Author: James Thomson Knight

Publisher: Cambridge University Press

Published: 1971-10-31

Total Pages: 141

ISBN-13: 0521081939

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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.

Book Synopsis Commutative Algebra by : James Thomson Knight

Download or read book Commutative Algebra written by James Thomson Knight and published by Cambridge University Press. This book was released on 1971-10-31 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Undergraduate Commutative Algebra

Author: Miles Reid

Publisher: Cambridge University Press

Published: 1995-11-30

Total Pages: 172

ISBN-13: 9780521458894

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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.

Book Synopsis Undergraduate Commutative Algebra by : Miles Reid

Download or read book Undergraduate Commutative Algebra written by Miles Reid and published by Cambridge University Press. This book was released on 1995-11-30 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction To Algebraic Geometry And Commutative Algebra

Author: Dilip P Patil

Publisher: World Scientific Publishing Company

Published: 2010-03-31

Total Pages: 220

ISBN-13: 9813100885

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This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics.Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses.

Book Synopsis Introduction To Algebraic Geometry And Commutative Algebra by : Dilip P Patil

Download or read book Introduction To Algebraic Geometry And Commutative Algebra written by Dilip P Patil and published by World Scientific Publishing Company. This book was released on 2010-03-31 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This introductory textbook for a graduate course in pure mathematics provides a gateway into the two difficult fields of algebraic geometry and commutative algebra. Algebraic geometry, supported fundamentally by commutative algebra, is a cornerstone of pure mathematics.Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. A selection is made from the wealth of material in the discipline, along with concise yet clear definitions and synopses.

Introduction To Commutative Algebra, An: From The Viewpoint Of Normalization

Author: Huishi Li

Publisher: World Scientific Publishing Company

Published: 2004-08-10

Total Pages: 188

ISBN-13: 9813106387

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Designed for a one-semester course in mathematics, this textbook presents a concise and practical introduction to commutative algebra in terms of normal (normalized) structure. It shows how the nature of commutative algebra has been used by both number theory and algebraic geometry. Many worked examples and a number of problem (with hints) can be found in the volume. It is also a convenient reference for researchers who use basic commutative algebra.

Book Synopsis Introduction To Commutative Algebra, An: From The Viewpoint Of Normalization by : Huishi Li

Download or read book Introduction To Commutative Algebra, An: From The Viewpoint Of Normalization written by Huishi Li and published by World Scientific Publishing Company. This book was released on 2004-08-10 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed for a one-semester course in mathematics, this textbook presents a concise and practical introduction to commutative algebra in terms of normal (normalized) structure. It shows how the nature of commutative algebra has been used by both number theory and algebraic geometry. Many worked examples and a number of problem (with hints) can be found in the volume. It is also a convenient reference for researchers who use basic commutative algebra.

Basic Commutative Algebra

Author: Balwant Singh

Publisher: World Scientific

Published: 2011

Total Pages: 405

ISBN-13: 9814313610

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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.

Book Synopsis Basic Commutative Algebra by : Balwant Singh

Download or read book Basic Commutative Algebra written by Balwant Singh and published by World Scientific. This book was released on 2011 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Commutative Algebra and Number Theory

Author: Sukumar Das Adhikari

Publisher: CRC Press

Published: 2001-11

Total Pages: 176

ISBN-13: 9780849309908

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This is an elementary introduction to algebra and number theory. The text begins by a review of groups, rings, and fields. The algebra portion addresses polynomial rings, UFD, PID, and Euclidean domains, field extensions, modules, and Dedckind domains. The number theory portion reviews elementary congruence, quadratic reciprocity, algebraic number fields, and a glimpse into the various aspects of that subject. This book could be used as a one semester course in graduate mathematics.

Book Synopsis An Introduction to Commutative Algebra and Number Theory by : Sukumar Das Adhikari

Download or read book An Introduction to Commutative Algebra and Number Theory written by Sukumar Das Adhikari and published by CRC Press. This book was released on 2001-11 with total page 176 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an elementary introduction to algebra and number theory. The text begins by a review of groups, rings, and fields. The algebra portion addresses polynomial rings, UFD, PID, and Euclidean domains, field extensions, modules, and Dedckind domains. The number theory portion reviews elementary congruence, quadratic reciprocity, algebraic number fields, and a glimpse into the various aspects of that subject. This book could be used as a one semester course in graduate mathematics.