Almost finite expansions of arbitrary semigroups
type: Item
instance of: scholarly article
title: Almost finite expansions of arbitrary semigroups
zbMATH Open document ID: 0546.20055
DOI: 10.1016/0022-4049(84)90092-6
author: J.-C. Birget
author: John L. Rhodes
published in: Journal of Pure and Applied Algebra
publication date: 1984-01-01T00:00:00Z
review text: The authors call general propositions global which are of the form: A semigroup S is a morphic image of a subsemigroup \(\bar S\) of a semigroup X (i.e., S divides X and \(\bar S\) is an expansion of S) and the oversemigroup X is built up from ''elementary'' semigroups using ''elementary'' operations. Two expansions of S are considered. These constructions are formed so that some of the methods of finite semigroup theory are applicable. Firstly, a semigroup S is said to be almost finite or finite-J-above if for all s in S there exist only finitely many t in S with \(t\geq_ Js\). In particular, every J-class of S is finite and each J-class has only finitely many J-classes above it. Two almost finite expansions are mentioned: The free expansion and the machine expansion. These are refined in Part II to expansions \(\bar S\) which are almost finite and, moreover, close to the original S. In Part III some applications are mentioned.
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 20M15
Mathematics Subject Classification ID: 20M35
zbMATH DE Number: 3869618
zbMATH Keywords: almost finite semigroups
zbMATH Keywords: expansions
zbMATH Keywords: J-classes
zbMATH Keywords: almost finite expansions
zbMATH Keywords: free expansion
zbMATH Keywords: machine expansion
reviewed by: Tero Harju
MaRDI profile type: Publication
full work available at URL: 0022-4049(84)90092-6
OpenAlex ID: W2079300096
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description: scientific article; zbMATH DE number 3869618