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    Undergraduate Commutative Algebra (London Mathematical Society Student Texts) (Paperback) By (author) Miles Reid, Series edited by J. W. Bruce

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    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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  • Full bibliographic data for Undergraduate Commutative Algebra

    Title
    Undergraduate Commutative Algebra
    Authors and contributors
    By (author) Miles Reid, Series edited by J. W. Bruce
    Physical properties
    Format: Paperback
    Number of pages: 168
    Width: 152 mm
    Height: 228 mm
    Thickness: 10 mm
    Weight: 260 g
    Language
    English
    ISBN
    ISBN 13: 9780521458894
    ISBN 10: 0521458897
    Classifications

    BIC E4L: MAT
    Nielsen BookScan Product Class 3: S7.8
    B&T Book Type: NF
    B&T Modifier: Region of Publication: 03
    Ingram Subject Code: SE
    Libri: I-SE
    B&T General Subject: 710
    B&T Modifier: Academic Level: 02
    B&T Modifier: Text Format: 06
    Warengruppen-Systematik des deutschen Buchhandels: 26280
    BISAC V2.8: SCI000000, MAT002000
    B&T Merchandise Category: UP
    BISAC V2.8: MAT014000
    BIC subject category V2: PBG
    DC20: 512.24
    LC subject heading:
    DC22: 512/.24, 512.24
    LC subject heading:
    LC classification: QA251.3 .R45 1995
    Thema V1.0: PBG
    Edition
    2
    Edition statement
    New.
    Illustrations note
    11 b/w illus.
    Publisher
    CAMBRIDGE UNIVERSITY PRESS
    Imprint name
    CAMBRIDGE UNIVERSITY PRESS
    Publication date
    12 December 2002
    Publication City/Country
    Cambridge
    Review quote
    '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
    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.