Rings and factorization
著者
書誌事項
Rings and factorization
Cambridge University Press, 1987
- : pbk
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注記
Includes index
内容説明・目次
内容説明
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.
目次
- 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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