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Steps in Commutative Algebra book cover, ISBN 9780521646239

Steps in Commutative Algebra

by Rodney Y. Sharp

ISBN13: 9780521646239
ISBN10: 0521646235
eBook ISBN(s): 9780511893520
Edition: 2nd
Format: Paperback
Copyright: 2001-01-22
Publisher: Cambridge University Press

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Summary

This introductory account of commutative algebra is aimed at students with a background only in basic algebra. Professor Sharp's book provides a good foundation from which the reader can proceed to more advanced works in commutative algebra or algebraic geometry. This new edition contains additional chapters on regular sequences and on Cohen-Macaulay rings.

Table of Contents

Preface to the 1st Edition

ix

Preface to the 2nd Edition

xii

Commutative rings and subrings

1

(17)

Ideals

18

(19)

Prime ideals and maximal ideals

37

(24)

Primary decomposition

61

(19)

Rings of fractions

80

(21)

Modules

101

(22)

Chain conditions on modules

123

(22)

Commutative Noetherian rings

145

(22)

More module theory

167

(18)

Modules over principal ideal domains

185

(23)

Canonical forms for square matrices

208

(12)

Some applications to field theory

220

(23)

Integral dependence on subrings

243

(21)

Affine algebras over fields

264

(24)

Dimension theory

288

(23)

Regular sequences and grade

311

(17)

Cohen-Macaulay rings

328

(17)

Bibliography

345

(2)

Index

347

Supplemental Materials

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