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Algebra: Third Edition
Saunders Mac Lane and Garrett Birkhoff
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AMS Chelsea Publishing
1988; 626 pp; hardcover
Volume: 330
ISBN-10: 0-8218-1646-2
ISBN-13: 978-0-8218-1646-2
List Price: US$65
Member Price: US$58.50
Order Code: CHEL/330.H
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This book presents modern algebra from first principles and is accessible to undergraduates or graduates. It combines standard materials and necessary algebraic manipulations with general concepts that clarify meaning and importance.

This conceptual approach to algebra starts with a description of algebraic structures by means of axioms chosen to suit the examples, for instance, axioms for groups, rings, fields, lattices, and vector spaces. This axiomatic approach--emphasized by Hilbert and developed in Germany by Noether, Artin, Van der Waerden, et al., in the 1920s--was popularized for the graduate level in the 1940s and 1950s to some degree by the authors' publication of A Survey of Modern Algebra. The present book presents the developments from that time to the first printing of this book. This third edition includes corrections made by the authors.

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Readership

Undergraduates and graduate students interested in algebra.

Reviews

"Nearly every ten years there seems to arrive a new edition of this now classical book the review of which the reviewer hardly can improve. The main advantage of the authors had been the introduction of thoroughly categorical concepts into algebra."

-- Zentralblatt MATH

"The book is clearly written, beautifully organized, and has an excellent and wide-ranging supply of exercises ... contains ample material for a full-year course on modern algebra at the undergraduate level."

-- Mathematical Reviews

Table of Contents

  • Sets, functions, and integers
  • Groups
  • Rings
  • Universal constructions
  • Modules
  • Vector spaces
  • Matrices
  • Special fields
  • Determinants and tensor products
  • Bilinear and quadratic forms
  • Similar matrices and finite abelian groups
  • Structure of groups
  • Galois theory
  • Lattices
  • Categories and adjoint functors
  • Multilinear algebra
  • Appendix: Affine and projective spaces
  • Bibliography
  • Index
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