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Steps in Commutative Algebra

Steps in Commutative Algebra

2nd Edition


Part of London Mathematical Society Student Texts

  • Date Published: January 2001
  • availability: Available
  • format: Paperback
  • isbn: 9780521646239

£ 44.99

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About the Authors
  • This introductory account of commutative algebra is aimed at advanced undergraduates and first year graduate students. Assuming only basic abstract algebra, it provides a good foundation in commutative ring theory, from which the reader can proceed to more advanced works in commutative algebra and algebraic geometry. The style throughout is rigorous but concrete, with exercises and examples given within chapters, and hints provided for the more challenging problems used in the subsequent development. After reminders about basic material on commutative rings, ideals and modules are extensively discussed, with applications including to canonical forms for square matrices. The core of the book discusses the fundamental theory of commutative Noetherian rings. Affine algebras over fields, dimension theory and regular local rings are also treated, and for this second edition two further chapters, on regular sequences and Cohen–Macaulay rings, have been added. This book is ideal as a route into commutative algebra.

    • Provides stepping stones to bridge gap from elementary prime factorization theory to the established books on commutative ring theory.
    • Straightforward introduction to commutative algebra (very important field, most books too hard)
    • Fully class tested and self-contained
    • Second edition of a popular text
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    Reviews & endorsements

    '… a very useful stepping-stone for students in their study of commutative algebra.' H. Mitsch, Universität Wien

    '… Sharp is an excellent guide, clearly aiming never to leave his readers floundering … This standard of care for his readers is maintained throughout the book … this is a superb guide to an attractive and important area of mathematics, and one from which I will derive pleasure as a retirement project. But it will never be an easy ride.' John Baylis, The Mathematical Gazette

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    Product details

    • Edition: 2nd Edition
    • Date Published: January 2001
    • format: Paperback
    • isbn: 9780521646239
    • length: 368 pages
    • dimensions: 230 x 161 x 24 mm
    • weight: 0.54kg
    • availability: Available
  • Table of Contents

    Prefaces to the 1st and 2nd editions
    1. Commutative rings and subrings
    2. Ideals
    3. Prime ideals and maximal ideals
    4. Primary decomposition
    5. Rings of fractions
    6. Modules
    7. Chain conditions on modules
    8. Commutative Noetherian rings
    9. More module theory
    10. Modules over principal ideal domains
    11. Canonical forms for square matrices
    12. Some applications to field theory
    13. Integral dependence on subrings
    14. Affine algebras over fields
    15. Dimension theory
    16. Regular sequences and grade
    17. Cohen–Macaulay rings

  • Author

    Rodney Y. Sharp, University of Sheffield

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