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Undergraduate Commutative Algebra

Undergraduate Commutative Algebra

$47.95

Part of London Mathematical Society Student Texts

  • Date Published: November 1995
  • availability: Available
  • format: Paperback
  • isbn: 9780521458894

$ 47.95
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About the Authors
  • 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
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    Reviews & endorsements

    '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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    Product details

    • Date Published: November 1995
    • format: Paperback
    • isbn: 9780521458894
    • length: 168 pages
    • dimensions: 227 x 153 x 10 mm
    • weight: 0.24kg
    • contains: 11 b/w illus.
    • availability: Available
  • Table of Contents

    Hello!
    1. Basics
    2. Modules
    3. Noetherian rings
    4. Finite extensions and Noether normalisation
    5. The nullstellensatz and spec A
    6. Rings of fractions S-1A and localisation
    7. Primary decomposition
    8. DVRs and normal integral domains
    9. Goodbye!
    Bibliography.

  • Author

    Miles Reid, University of Warwick

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