Rings and Factorization

Klappentext This textbook is an introduction to the concept of factorisation and its application to problems in algebra and number theory. Zusammenfassung 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. Inhaltsverzeichnis 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.

Zusammenfassung
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.

Inhalt
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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