An Introductory Course in Commutative Algebra

Paperback | May 1, 1998

byA. W. Chatters, C. R. Hajarnavis

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This book aims to be a concise introduction to topics in commutative algebra, with an emphasis on worked examples and applications. It combines elegant algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields which hasimportant uses in other branches of science. Topics covered include rings and Euclidean rings, the four-squares theorem, fields and field extensions, finite cyclic groups and finite fields. The material covered in this book prepares the way for the further study of abstract algebra, but it couldalso form the basis of an entire course.

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This book aims to be a concise introduction to topics in commutative algebra, with an emphasis on worked examples and applications. It combines elegant algebraic theory with applications to number theory, problems in classical Greek geometry, and the theory of finite fields which hasimportant uses in other branches of science. Topics...

A. W. Chatters is at University of Bristol. C. R. Hajarnavis is at University of Warwick.

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Format:PaperbackDimensions:152 pages, 9.21 × 6.14 × 0.35 inPublished:May 1, 1998Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198501447

ISBN - 13:9780198501442

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Extra Content

Table of Contents

1. Rings2. Euclidean rings3. Highest common factor4. The four-squares theorem5. Fields and polynomials6. Unique factorization domains7. Field of quotients of an integral domain8. Factorization of polynomials9. Fields and field extensions10. Finite cyclic groups and finite fields11. Algebraic numbers12. Ruler and Compass constructions13. Homomorphisms, ideals and factor rings14. Principal ideal domains and a method for constructing fields15. Finite fieldsSolutions to selected exercisesReferences

Editorial Reviews

Immaculately organised, the text glides seamlessly from the concrete to the abstrat; it is carefully written without being pedantic and all of the right motivational and cautinoary noises are made as intuition and feel for each new concept is developed.