Undergraduate Commutative Algebra (London Mathematical Society Student Texts)

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9780521452557: Undergraduate Commutative Algebra (London Mathematical Society Student Texts)
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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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Showing the link between commutative ring theory and algebraic geometry, this book contrasts the methods and ideology of modern abstract algebra with concrete applications in algebraic geometry and number theory. It is ideal for anyone seeking a primer on commutative algebra.

Review:

'It gives a fresh picture of the subject for a new generation of students.' P. Scnezel, Zentralblatt fur Mathematik

'The author takes care to explain the geometric and number theoretic meaning of the algebraic methods and results presented. This makes the book perhaps more demanding, but surely much more interesting than the standard ones.' European Mathematical Society Newsletter

'Besides the usual topics ... there are some welcome geometrical illustrations, as well as some homespun philosophy.' Mathematica

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9780521458894: Undergraduate Commutative Algebra (London Mathematical Society Student Texts)

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ISBN 10:  0521458897 ISBN 13:  9780521458894
Publisher: Cambridge University Press, 1996
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9784000051897: Commutative ring theory Introduction (2000) ISBN: 400005189X [Japanese Import]

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Book Description 1995. Hardback. Condition: NEW. 9780521452557 This listing is a new book, a title currently in-print which we order directly and immediately from the publisher. For all enquiries, please contact Herb Tandree Philosophy Books directly - customer service is our primary goal. Seller Inventory # HTANDREE0458045

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2002. Hardback. Condition: New. Language: English. Brand new Book. 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. Seller Inventory # APC9780521452557

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Book Description CAMBRIDGE UNIVERSITY PRESS, United Kingdom, 2002. Hardback. Condition: New. Language: English. Brand new Book. 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. Seller Inventory # APC9780521452557

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Book Description Cambridge University Press. Hardcover. Condition: New. 168 pages. Dimensions: 8.9in. x 6.1in. x 0.7in.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. This item ships from multiple locations. Your book may arrive from Roseburg,OR, La Vergne,TN. Hardcover. Seller Inventory # 9780521452557

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