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Rings and Factorization - David Sharpe

Rings and Factorization

Paperback Published: 9th November 1987
ISBN: 9780521337182
Number Of Pages: 124

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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.

Preface
Introduction
Rings
Introduction
Binary operations
Definition of a ring
Homomorphisms, subrings and isomorphisms
Integral domains
Fields
Residue-class rings
Factorization
Introduction
Unique factorization domains
Euclidean domains
Greatest common divisors
Prime elements
Euclidean domains are UFDs
The two-square theorem
Factorization of polynomials
An application of UFD's to determinantal identities
Postscript
Partial solutions to exercises
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521337182
ISBN-10: 0521337186
Audience: Tertiary; University or College
Format: Paperback
Language: English
Number Of Pages: 124
Published: 9th November 1987
Publisher: CAMBRIDGE UNIV PR
Country of Publication: GB
Dimensions (cm): 21.59 x 13.97  x 0.74
Weight (kg): 0.17

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