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An Introductory Course in Commutative Algebra~tqw~ darksiderg

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An Introductory Course in Commutative Algebra
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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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