An Introductory Course in Commutative Algebra~tqw~ darksiderg

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  An Introductory Course in Commutative Algebra~tqw~ darksiderg
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• Added:
  10/01/2008
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  *******************************************************************************<br /> An Introductory Course in Commutative Algebra <br /> *******************************************************************************<br /> <br /> -------------------------------------------------------------------------------<br /> General Information<br /> -------------------------------------------------------------------------------<br /> Type.................: Ebook<br /> Part Size............: 20,699,718 bytes<br /> <br /> <br /> <br /> <br /> -------------------------------------------------------------------------------<br /> Post Information<br /> -------------------------------------------------------------------------------<br /> Posted by............: ~tqw~<br /> <br /> -------------------------------------------------------------------------------<br /> Release Notes<br /> -------------------------------------------------------------------------------<br /> This book is a concise and carefully written introduction to topics in <br /> commutative algebra, with an emphasis on worked examples and applications. The <br /> elegant algebraic theory is combined with applications to number theory, <br /> problems in classical Greek geometry, and the theory of finite fields, which has <br /> important uses in other branches of science. Topics covered include an <br /> introduction to rings and Euclidean rings, UFDs and PIDs, factorization of <br /> polynomials, fields and field extensions, and algebraic numbers. This book could <br /> form a springboard to further study of abstract algebra, but is also eminently <br /> suitable as the course text for an entire undergraduate course. <br /> <br /> Table Of Contents<br /> <br /> List of symbols viii<br /> 1 Rings 1<br /> 2 Euclidean rings 10<br /> 3 Highest common factor 17<br /> 4 The four-squares theorem 23<br /> 5 Fields and polynomials 30<br /> 6 Unique factorization domains 35<br /> 7 Field of quotients of an integral domain 43<br /> 8 Factorization of polynomials 46<br /> 9 Fields and field extensions 60<br /> 10 Finite cyclic groups and finite fields 69<br /> 11 Algebraic numbers 77<br /> 12 Ruler-and-compass constructions 87<br /> 13 Homomorphisms, ideals, and factor rings 102<br /> 14 Principal ideal domains and a method<br /> for constructing fields 116<br /> 15 Finite fields 124<br /> Solutions to selected exercises 129<br /> References 141<br /> Index 143<br /> <br /> Product Details<br /> <br /> * ISBN: 019853423X<br /> * ISBN-13: 9780198534235<br /> * Format: Hardcover, 160pp<br /> * Publisher: Oxford University Press, USA<br /> * Pub. Date: July 1998<br /> <br /> -------------------------------------------------------------------------------<br /> Install Notes<br /> -------------------------------------------------------------------------------<br /> PDF Reader<br />
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