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Undergraduate Commutative Algebra - 95 edition

Undergraduate Commutative Algebra (ISBN10: 0521458897; ISBN13: 9780521458894)
ISBN13: 978-0521458894
ISBN10: 0521458897

This edition has also been released as:
ISBN13: 978-0521452557
ISBN10: 0521452554

Summary: 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 s
pace. 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.
  • Direct competitor to Atiyah and Macdonald but undercuts it easily
  • Informal and humorous
  • Well-known author
...show more
Summary: 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.
  • Direct competitor to Atiyah and Macdonald but undercuts it easily
  • Informal and humorous
  • Well-known author
...show less

Edition/Copyright: 95
Cover:
Publisher: Cambridge University Press
Year Published: 1995
International: No

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