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The Algebraic Theory of Semigroups, Volume II
A. H. Clifford and G. B. Preston

Mathematical Surveys and Monographs
1967; 352 pp; softcover
Volume: 7
Reprint/Revision History:
reprinted with corrections 1971; third printing 1988
ISBN-10: 0-8218-0272-0
ISBN-13: 978-0-8218-0272-4
List Price: US$63
Member Price: US$50.40
Order Code: SURV/7.2
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This book, along with Volume I, which appeared previously, presents a survey of the structure and representation theory of semigroups. Volume II goes more deeply than was possible in Volume I into the theories of minimal ideals in a semigroup, inverse semigroups, simple semigroups, congruences on a semigroup, and the embedding of a semigroup in a group.

Among the more important recent developments of which an extended treatment is presented are B. M. Sain's theory of the representations of an arbitrary semigroup by partial one-to-one transformations of a set, L. Redei's theory of finitely generated commutative semigroups, J. M. Howie's theory of amalgamated free products of semigroups, and E. J. Tully's theory of representations of a semigroup by transformations of a set. Also a full account is given of Malcev's theory of the congruences on a full transformation semigroup.

Table of Contents

  • Minimal ideals and minimal conditions
  • Inverse semigroups
  • Simple semigroups
  • Finite presentations of semigroups and free products with amalgamations
  • Congruences
  • Representation by transformations of a set
  • Embedding a semigroup in a group
  • Bibliography
  • Errata to volume I
  • Author index
  • Index
  • Appendix
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