Bifree locally inverse semigroups as expansions.
type: Item
instance of: scholarly article
title: Bifree locally inverse semigroups as expansions.
zbMATH Open document ID: 1066.20060
author: Bernd Billhardt
published in: Journal of Algebra
publication date: 2005-02-22T00:00:00Z
review text: In a preceding paper [Stud.~Sci.~Math.~Hung.~41, No. 1, 39--58 (2004; Zbl 1070.20074)], the author assigns to each completely simple semigroup \(S\) an expansion \({\mathcal C}(S)\) which is a locally inverse semigroup and which coincides with the Birget-Rhodes expansion in case \(S\) is a group. In the present paper, the author further explores the properties of \({\mathcal C}(S)\). The main result states that if \(S\) is the bifree completely simple semigroup on a set \(X\) then \({\mathcal C}(S)\) contains a copy of the bifree locally inverse semigroup on \(X\). As a consequence, new proofs of two classical results by Pastijn are obtained: (i) each locally inverse semigroup divides a semidirect product of a semilattice by a completely simple semigroup; (ii) each locally inverse semigroup divides a perfect rectangular band of inverse monoids.
reviewed by: K. Auinger
Mathematics Subject Classification ID: 20M18
Mathematics Subject Classification ID: 20M17
Mathematics Subject Classification ID: 20M05
zbMATH DE Number: 2136594
zbMATH Keywords: Birget-Rhodes expansions
zbMATH Keywords: bifree completely simple semigroups
zbMATH Keywords: bifree locally inverse semigroups
zbMATH Keywords: perfect rectangular bands of inverse monoids
MaRDI profile type: Publication
full work available at URL: j.jalgebra.2004.09.005
OpenAlex ID: W1987350639
cites work: The bifree locally inverse semigroup on a set
cites work: On the bifree locally inverse semigroup
cites work: A System of Bi-Identities for Locally Inverse Semigroups
cites work: Q4220451
cites work: On a wreath product embedding and idempotent pure congruences on inverse semigroups
cites work: Q2754915
cites work: Expansions of completely simple semigroups
cites work: A factorization of dual prehomomorphisms and expansions of inverse semigroups
cites work: Group theory via global semigroup theory
cites work: Identities for existence varieties of regular semigroups
cites work: Q4846425
cites work: A new approach in the theory of orthodox semigroups
cites work: PARTIAL ACTIONS OF GROUPS
cites work: Q4537454
cites work: Expansions of inverse semigroups
cites work: Perfect rectangular bands of inverse monoids
cites work: Regular expansions of completely simple semigroups
cites work: The free rectangular band of inverse semigroups on a set
cites work: Q3889272
cites work: Q3964785
cites work: The Structure of Pseudo-Inverse Semigroups
cites work: Straight Locally Inverse Semigroups
cites work: Q3337662
cites work: Q4170918
cites work: A note on Birget-Rhodes expansion of groups
cites work: THE EXISTENCE OF E-FREE OBJECTS IN E-VARIETIES OF REGULAR SEMIGROUPS
DOI: 10.1016/J.JALGEBRA.2004.09.005
description: scientific article; zbMATH DE number 2136594