Finite images and elementary equivalence of completely regular inverse semigroups
type: Item
instance of: scholarly article
title: Finite images and elementary equivalence of completely regular inverse semigroups
zbMATH Open document ID: 0817.20061
DOI: 10.1007/BF03025773
author: F. Oger
published in: Semigroup Forum
publication date: 1993-03-01T00:00:00Z
full work available at URL: https://eudml.org/doc/135195
review text: The author extends his result [Proc. Am. Math. Soc. 103, 1041-1048 (1988; Zbl 0642.20001)] and shows that if two diagrams of groups \(G\), \(H\) are finite unions of finitely generated abelian-by-finite groups, then \(G\) and \(H\) are elementarily equivalent iff they have the same finite images. Using an interpretation of completely regular inverse semigroups in terms of diagrams of groups, he proves the analogous theorem about completely regular inverse semigroups which are disjoint unions of finitely generated abelian-by-finite groups. Finally, the author considers diagrams of groups which consist of one group and one or several endomorphisms of this group. In particular, he investigates modules over not necessarily commutative rings.
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20A15
zbMATH DE Number: 126124
zbMATH Keywords: group endomorphisms
zbMATH Keywords: diagrams of groups
zbMATH Keywords: abelian-by-finite groups
zbMATH Keywords: elementarily equivalent groups
zbMATH Keywords: completely regular inverse semigroups
reviewed by: B. Pondělíček
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 126124