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Prime decomposition theorem for arbitrary semigroups: General holonomy decomposition and synthesis theorem. (English) Zbl 0679.20056
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.
Reviewer: L.Potemkin

MSC:
20M10 General structure theory for semigroups
20M50 Connections of semigroups with homological algebra and category theory
20M05 Free semigroups, generators and relations, word problems
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