Undergraduate Commutative Algebra
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Undergraduate Commutative Algebra by Miles Reid
Book DescriptionCommutative 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.
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Book DetailsISBN: 9780521452557
(228mm x 152mm x 13mm)
Imprint: Cambridge University Press
Publisher: Cambridge University Press
Publish Date: 30-Nov-1995
Country of Publication: United Kingdom
Books By Author Miles Reid
Basic Algebraic Geometry, Hardback (September 2013)
Basic Algebraic Geometry 2
Geometry and Topology, Paperback (November 2005)
An introduction to the ideas of geometry and includes generous helpings of simple explanations and examples.
Number Theory and Algebraic Geometry, Paperback (January 2004)
This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.
Explicit Birational Geometry of 3-folds, Paperback (July 2000)» View all books by Miles Reid
This volume, first published in 2000, is an integrated suite of papers centred around applications of Mori theory to birational geometry.
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