A topological approach to inverse and regular semigroups.
type: Item
instance of: scholarly article
title: A topological approach to inverse and regular semigroups.
zbMATH Open document ID: 1057.20043
author: Benjamin Steinberg
published in: Pacific Journal of Mathematics
publication date: 2004-09-16T00:00:00Z
review text: In this substantial paper the author revisits the ordered groupoid approach to inverse and regular semigroups with a topological slant. Specifically it is proved that any ordered groupoid can be realized as the fundamental ordered groupoid of an ordered 2-complex. It is shown how to construct an ordered groupoid presentation from any inverse semigroup presentation. The so-called Schützenberger complex of an inverse semigroup presentation is introduced and it plays a role in the theory similar to that played by the Cayley complex in group theory. A new proof that a maximal subgroup of a full amalgam of regular semigroups has a certain graph of groups composition allows proof and extension of a range of standard results on strong embeddability of regular semigroup amalgams. Certain results in the category of inverse semigroups and pre-homomorphisms are likewise obtained.
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M05
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 22A15
Mathematics Subject Classification ID: 57M07
zbMATH DE Number: 2101057
zbMATH Keywords: 2-complexes
zbMATH Keywords: inverse semigroups
zbMATH Keywords: regular semigroups
zbMATH Keywords: amalgams
zbMATH Keywords: ordered groupoids
zbMATH Keywords: presentations
reviewed by: Peter M. Higgins
MaRDI profile type: Publication
full work available at URL: pjm.2003.208.367
OpenAlex ID: W2064515284
DOI: 10.2140/PJM.2003.208.367
description: scientific article; zbMATH DE number 2101057