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 [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.
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© 2011 Springer Science+Business Media, LLC
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Högnäs, G., Mukherjea, A. (2011). Semigroups. In: Probability Measures on Semigroups. Probability and Its Applications. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-77548-7_1
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DOI: https://doi.org/10.1007/978-0-387-77548-7_1
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Publisher Name: Springer, Boston, MA
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Online ISBN: 978-0-387-77548-7
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