Undergraduate Commutative Algebra

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Cambridge University Press, Nov 30, 1995 - Mathematics - 153 pages
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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.

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g Discussion of contents
g Plenty of prime ideals
g Exact sequences
Finite extensions and Noether normalisation
The Nullstellensatz and Spec A
Exercises to Chapter 5
Exercises to Chapter 6
Exercises to Chapter 7
Exercises to Chapter 8
Akizukis example

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Elementary Algebraic Geometry
Klaus Hulek
No preview available - 2003
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About the author (1995)

Miles Reid is a Professor of Mathematics at the Mathematics Institute, University of Warwick.

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