Introduction to Algebraic Geometry and Commutative Algebra

Author: Dilip P. Patil,Uwe Storch

Publisher: World Scientific

ISBN: 9814304573

Category: Mathematics

Page: 207

View: 1824

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Along the lines developed by Grothendieck, this book delves into the rich interplay between algebraic geometry and commutative algebra. With concise yet clear definitions and synopses a selection is made from the wealth of meterial in the disciplines including the Riemann-Roch theorem for arbitrary projective curves."--pub. desc.
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Commutative Algebra

With a View Toward Algebraic Geometry

Author: David Eisenbud,Professor David Eisenbud

Publisher: Springer Science & Business Media

ISBN: 9780387942698

Category: Mathematics

Page: 785

View: 6896

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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.
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Algebraic Geometry and Commutative Algebra

Author: Siegfried Bosch

Publisher: Springer Science & Business Media

ISBN: 1447148290

Category: Mathematics

Page: 504

View: 2104

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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. Moreover, Grothendieck’s schemes invented in the late 1950s allowed the application of algebraic-geometric methods in fields that formerly seemed to be far away from geometry, like algebraic number theory. The new techniques paved the way to spectacular progress such as the proof of Fermat’s Last Theorem by Wiles and Taylor. The scheme-theoretic approach to algebraic geometry is explained for non-experts. More advanced readers can use the book to broaden their view on the subject. A separate part deals with the necessary prerequisites from commutative algebra. On a whole, the book provides a very accessible and self-contained introduction to algebraic geometry, up to a quite advanced level. Every chapter of the book is preceded by a motivating introduction with an informal discussion of the contents. Typical examples and an abundance of exercises illustrate each section. This way the book is an excellent solution for learning by yourself or for complementing knowledge that is already present. It can equally be used as a convenient source for courses and seminars or as supplemental literature.
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Algebraic Geometry for Associative Algebras

Author: Freddy Van Oystaeyen

Publisher: CRC Press

ISBN: 9780824704247

Category: Mathematics

Page: 302

View: 6666

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This work focuses on the association of methods from topology, category and sheaf theory, algebraic geometry, noncommutative and homological algebras, quantum groups and spaces, rings of differential operation, Cech and sheaf cohomology theories, and dimension theories to create a blend of noncommutative algebraic geometry. It offers a scheme theory that sustains the duality between algebraic geometry and commutative algebra to the noncommutative level.
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Undergraduate Commutative Algebra

Author: Reid Miles,Miles Reid

Publisher: Cambridge University Press

ISBN: 9780521458894

Category: Mathematics

Page: 153

View: 653

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In this well-written introduction to commutative algebra, the author shows the link between commutative ring theory and algebraic geometry. In addition to standard material, the book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. Professor Reid begins with a discussion of modules and Noetherian rings before moving on to finite extensions and the Noether normalization. Sections on the nullstellensatz and rings of fractions precede sections on primary decomposition and normal integral domains. This book is ideal for anyone seeking a primer on commutative algebra.
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Commutative Ring Theory

Author: H. Matsumura

Publisher: Cambridge University Press

ISBN: 9780521367646

Category: Mathematics

Page: 320

View: 2503

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

Author: O. Zariski,P. Samuel

Publisher: Springer Science & Business Media

ISBN: 9780387901718

Category: Mathematics

Page: 416

View: 2402

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From the Preface: "topics are: (a) valuation theory; (b) theory of polynomial and power series rings (including generalizations to graded rings and modules); (c) local algebra... the algebro-geometric connections and applications of the purely algebraic material are constantly stressed and abundantly scattered throughout the exposition. Thus, this volume can be used in part as an introduction to some basic concepts and the arithmetic foundations of algebraic geometry."
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The Red Book of Varieties and Schemes

Author: David Mumford

Publisher: Springer

ISBN: 3662215810

Category: Mathematics

Page: 315

View: 6583

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"The book under review is a reprint of Mumford's famous Harvard lecture notes, widely used by the few past generations of algebraic geometers. Springer-Verlag has done the mathematical community a service by making these notes available once again.... The informal style and frequency of examples make the book an excellent text." (Mathematical Reviews)
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Algebraic Geometry

A First Course

Author: Joe Harris,JOE AUTOR HARRIS

Publisher: Springer Science & Business Media

ISBN: 0387977163

Category: Mathematics

Page: 328

View: 9833

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"This book succeeds brilliantly by concentrating on a number of core topics...and by treating them in a hugely rich and varied way. The author ensures that the reader will learn a large amount of classical material and perhaps more importantly, will also learn that there is no one approach to the subject. The essence lies in the range and interplay of possible approaches. The author is to be congratulated on a work of deep and enthusiastic scholarship." --MATHEMATICAL REVIEWS
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Commutative Algebra

Chapters 1-7

Author: N. Bourbaki

Publisher: Springer Science & Business Media

ISBN: 9783540642398

Category: Mathematics

Page: 625

View: 9693

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This is the softcover reprint of the English translation of 1972 (available from Springer since 1989) of the first 7 chapters of Bourbaki's 'Algèbre commutative'. It provides a very complete treatment of commutative algebra, enabling the reader to go further and study algebraic or arithmetic geometry. The first 3 chapters treat in succession the concepts of flatness, localization and completions (in the general setting of graduations and filtrations). Chapter 4 studies associated prime ideals and the primary decomposition. Chapter 5 deals with integers, integral closures and finitely generated algebras over a field (including the Nullstellensatz). Chapter 6 studies valuation (of any rank), and the last chapter focuses on divisors (Krull, Dedekind, or factorial domains) with a final section on modules over integrally closed Noetherian domains, not usually found in textbooks. Useful exercises appear at the ends of the chapters.
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