Basic Abstract Algebra

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Overview

In addition to many new problems for practice and challenge, this edition of a self-contained graduate text on abstract algebra contains an introduction to lattices, a new chapter on tensor products and a discussion of the new 1993 approach to the celebrated Lasker-Noether theorem.
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Editorial Reviews

From the Publisher
"...a thorough and surprisingly clean-cut survey of the group/ring/field troika which manages to convey the idea of algebra as a unified enterprise." Ian Stewart, New Scientist
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Product Details

  • ISBN-13: 9780521311076
  • Publisher: Cambridge University Press
  • Publication date: 4/30/1986
  • Pages: 476
  • Product dimensions: 6.06 (w) x 9.25 (h) x 0.91 (d)

Table of Contents

Preface to the second edition
Preface to the first edition
Glossary of symbols
Ch. 1 Sets and mappings 3
Ch. 2 Integers, real numbers, and complex numbers 30
Ch. 3 Matrices and determinants 39
Ch. 4 Groups 61
Ch. 5 Normal subgroups 91
Ch. 6 Normal series 120
Ch. 7 Permutation groups 129
Ch. 8 Structure theorems of groups 138
Ch. 9 Rings 159
Ch. 10 Ideals and homomorphisms 179
Ch. 11 Unique factorization domains and euclidean domains 212
Ch. 12 Rings of fractions 224
Ch. 13 Integers 233
Ch. 14 Modules and vector spaces 246
Ch. 15 Algebraic extensions of fields 281
Ch. 16 Normal and separable extensions 300
Ch. 17 Galois theory 322
Ch. 18 Applications of Galois theory to classical problems 340
Ch. 19 Noetherian and artinian modules and rings 367
Ch. 20 Smith normal form over a PID and rank 392
Ch. 21 Finitely generated modules over a PID 402
Ch. 22 Tensor products 426
Solutions to odd-numbered problems 438
Selected bibliography 476
Index 477
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Customer Reviews

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  • Anonymous

    Posted March 20, 2002

    my favorite

    This is a very elementary book on abstract algebra, clearly written, easy to study from, and thus, suitable for self-study. The authors provide lots of examples, and many solutions to the exercises. All the topics are quite standard for an undergraduate course in abstract algebra. The price of the paperback edition is more than appropriate. A true jewel of algebra. Highly recommended.

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  • Anonymous

    Posted March 29, 2012

    No text was provided for this review.

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