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Rings and Factorization

$51.99 (C)

  • Date Published: August 1987
  • availability: Available
  • format: Paperback
  • isbn: 9780521337182

$ 51.99 (C)
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  • This textbook is an introduction to the concept of factorization and its application to problems in algebra and number theory. With the minimum of prerequisites, the reader is introduced to the notion of rings, fields, prime elements and unique factorization. The author shows how concepts can be applied to a variety of examples such as factorizing polynomials, finding determinants of matrices and Fermat's 'two-squares theorem'. Based on an undergraduate course given at the University of Sheffield, Dr Sharpe has included numerous examples which demonstrate how frequently these ideas are useful in concrete, rather than abstract, settings. The book also contains many exercises of varying degrees of difficulty together with hints and solutions. Second and third year undergraduates will find this a readable and enjoyable account of a subject lying at the heart of much of mathematics.

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    Product details

    • Date Published: August 1987
    • format: Paperback
    • isbn: 9780521337182
    • length: 124 pages
    • dimensions: 216 x 140 x 7 mm
    • weight: 0.17kg
    • availability: Available
  • Table of Contents

    Preface
    Introduction
    Part I: Rings
    1. Introduction
    2. Binary operations
    3. Definition of a ring
    4. Homomorphisms, subrings and isomorphisms
    5. Integral domains
    6. Fields
    7. Residue-class rings
    Part II: Factorization
    8. Introduction
    9. Unique factorization domains
    10. Euclidean domains
    11. Greatest common divisors
    12. Prime elements
    13. Euclidean domains are UFDs
    14. The two-square theorem
    15. Factorization of polynomials
    16. An application of UFD's to determinantal identities
    Postscript
    Partial solutions to exercises
    References
    Index.

  • Author

    David Sharpe

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