Description

Book Synopsis
This textbook is an introduction to the concept of factorization and its application to problems in algebra and number theory. 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.

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.

Rings and Factorization

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    A Paperback by David Sharpe

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      Publisher: Cambridge University Press
      Publication Date: Publication Date: 8/28/1987 12:00:00 AM
      ISBN13: 9780521337182, 978-0521337182
      ISBN10: 0521337186
      Also in:
      Algebra

      Description

      Book Synopsis
      This textbook is an introduction to the concept of factorization and its application to problems in algebra and number theory. 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.

      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.

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