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Zbl 0679.20056
Henckell, Karsten; Lazarus, Susan; Rhodes, John
Prime decomposition theorem for arbitrary semigroups: General holonomy decomposition and synthesis theorem. (English)
[J] J. Pure Appl. Algebra 55, No.1-2, 127-172 (1988). ISSN 0022-4049

The authors generalize the holonomy form of the Prime Decomposition Theorem of Krohn and Rhodes for finite semigroups to arbitrary infinite semigroups. This is accomplished by embedding $\hat S$ into an infinite Zeiger wreath product after applying the triple Schützenberger product which makes S finite-J-above (Rhodes' theorem). Here finite-J-above means every element has only a finite number of divisors.
[L.Potemkin]

MSC 2000:: *20M10 General structure theory of semigroups
20M50 Connections of semigroups with homological algebra
20M05 Free semigroups

Keywords: Prime Decomposition Theorem; infinite Zeiger wreath product; triple Schützenberger product

Cited in: Zbl 0797.20053

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