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


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.


Simple Semigroup Topological Semigroup Nonnegative Matrice Primitive Idempotent Minimal Rank 
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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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