Wreath products of algebras: Generalizing the Krohn-Rhodes theorem to arbitrary algebras
type: Item
instance of: scholarly article
title: Wreath products of algebras: Generalizing the Krohn-Rhodes theorem to arbitrary algebras
zbMATH Open document ID: 0840.08001
DOI: 10.1007/BF02574084
author: Joel VanderWerf
published in: Semigroup Forum
publication date: 1996-06-06T00:00:00Z
full work available at URL: https://eudml.org/doc/135436
review text: The Krohn-Rhodes Prime Decomposition Theorem describes the basic semigroups needed in a wreath product decomposition of a finite semigroup. The author's goal has been to extend this famous theorem to arbitrary finite algebras, and for this purpose possible generalizations of the central notions of the Krohn-Rhodes theory, such as wreath products, the corresponding decompositions, aperiodicity and solvability, are defined and studied. Difficulties associated with the generalization are pinpointed and some open problems are posed. Connections with the Hobby-McKenzie theory of tame congruences are also noted. The paper is actually an extended abstract of the author's dissertation, and hence all proofs and many details have been omitted.
Mathematics Subject Classification ID: 08A05
Mathematics Subject Classification ID: 08A40
zbMATH DE Number: 836811
zbMATH Keywords: tame congruence
zbMATH Keywords: Krohn-Rhodes prime decomposition theorem
zbMATH Keywords: wreath product decomposition
zbMATH Keywords: finite algebras
zbMATH Keywords: aperiodicity
zbMATH Keywords: solvability
reviewed by: Magnus Steinby
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 836811