Prime decomposition theorem for arbitrary semigroups: General holonomy decomposition and synthesis theorem
type: Item
instance of: scholarly article
title: Prime decomposition theorem for arbitrary semigroups: General holonomy decomposition and synthesis theorem
zbMATH Open document ID: 0679.20056
DOI: 10.1016/0022-4049(88)90043-6
author: Karsten Henckell
author: Susan Lazarus
author: John L. Rhodes
published in: Journal of Pure and Applied Algebra
publication date: 1988-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 4112902
zbMATH Keywords: Prime Decomposition Theorem
zbMATH Keywords: infinite Zeiger wreath product
zbMATH Keywords: triple Schützenberger product
reviewed by: L.V.Potemkin
MaRDI profile type: Publication
full work available at URL: 0022-4049(88)90043-6
OpenAlex ID: W1966871890
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description: scientific article; zbMATH DE number 4112902