Semigroups

  • Göran Högnäs
  • Arunava Mukherjea
Part of the The University Series in Mathematics book series (USMA)

Abstract

Chapter 1 contains the basics of semigroups: definitions, elementary concepts, and fundamental examples. We assume some familiarity with standard notions of point-set topology [see Kelley (1955), Mukherjea and Pothoven (1984)]; the algebraic portions of Chapter 1 are however completely self-contained. Without going into any detail whatsoever, it is perhaps prudent to remark at this point that our main interest centers around asymptotics, invariance questions, etc. Our treatment is a reflection of this. We concentrate on algebraic concepts corresponding to such phenomena as absorption, stability, and invariance: zeros, simple semigroups, minimal ideals, maximal subgroups, and so on. We strive to keep digressions at a minimum. Clifford and Preston (1961) offer a wealth of information on all aspects of algebraic semigroups, and this text is recommended to any reader interested in a much more elaborate treatment of this fascinating subject.

Keywords

Simple Semigroup Topological Semigroup Nonnegative Matrice Primitive Idempotent Minimal Rank 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1995

Authors and Affiliations

  • Göran Högnäs
    • 1
  • Arunava Mukherjea
    • 2
  1. 1.Åbo Akademi UniversityÅboFinland
  2. 2.University of South FloridaTampaUSA

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