Part of the Probability and Its Applications book series (PIA)


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 [124, 167]); the algebraic portions of Chap. 1 are, however, completely self-contained. Without going into any details 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 the digressions at a minimum. Clifford and Preston [43] offers 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.


Left Ideal Simple Semigroup Topological Semigroup Nonnegative Matrice Primitive Idempotent 
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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Åbo Akademi UniversityÅboFinland
  2. 2.Department of MathematicsUniversity of Texas – Pan AmericanEdinburgUSA

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