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                An Introductory Course in Commutative Algebra 

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                              General Information

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Type.................: Ebook

Part Size............: 20,699,718 bytes









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Posted by............: ~tqw~



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                                 Release Notes

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This book is a concise and carefully written introduction to topics in 

commutative algebra, with an emphasis on worked examples and applications. The 

elegant algebraic theory is combined with applications to number theory, 

problems in classical Greek geometry, and the theory of finite fields, which has 

important uses in other branches of science. Topics covered include an 

introduction to rings and Euclidean rings, UFDs and PIDs, factorization of 

polynomials, fields and field extensions, and algebraic numbers. This book could 

form a springboard to further study of abstract algebra, but is also eminently 

suitable as the course text for an entire undergraduate course. 



Table Of Contents



List of symbols viii

1 Rings 1

2 Euclidean rings 10

3 Highest common factor 17

4 The four-squares theorem 23

5 Fields and polynomials 30

6 Unique factorization domains 35

7 Field of quotients of an integral domain 43

8 Factorization of polynomials 46

9 Fields and field extensions 60

10 Finite cyclic groups and finite fields 69

11 Algebraic numbers 77

12 Ruler-and-compass constructions 87

13 Homomorphisms, ideals, and factor rings 102

14 Principal ideal domains and a method

for constructing fields 116

15 Finite fields 124

Solutions to selected exercises 129

References 141

Index 143



Product Details



    * ISBN: 019853423X

    * ISBN-13: 9780198534235

    * Format: Hardcover, 160pp

    * Publisher: Oxford University Press, USA

    * Pub. Date: July 1998



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