Absolute flatness of the full transformation semigroups
type: Item
instance of: scholarly article
title: Absolute flatness of the full transformation semigroups
zbMATH Open document ID: 0661.20044
DOI: 10.1016/0021-8693(88)90037-3
author: Kunitaka Shoji
published in: Journal of Algebra
publication date: 1988-01-01T00:00:00Z
review text: \({\mathcal T}_ X\) denotes the full transformation semigroup on a set X. A monoid S is defined to be left absolutely flat if every left S-set is flat. This paper is devoted to a proof of the result that \({\mathcal T}_ X\) is left absolutely flat if and only if X is finite. This, together with previous results by the author and others, yield the fact that \({\mathcal T}_ X\) has the strong representation property if and only if X is finite and also that \({\mathcal T}_ X\) is an amalgamation base in the class of all semigroups whenever X is finite.
Mathematics Subject Classification ID: 20M20
Mathematics Subject Classification ID: 20M50
zbMATH DE Number: 4079761
zbMATH Keywords: full transformation semigroup
zbMATH Keywords: left absolutely flat
zbMATH Keywords: left S-set
zbMATH Keywords: strong representation property
zbMATH Keywords: amalgamation base
Wikidata QID: Q112879903
reviewed by: jun. Kenneth D. Magill
MaRDI profile type: Publication
full work available at URL: 0021-8693(88)90037-3
OpenAlex ID: W1967355648
cites work: Q3693722
cites work: Absolutely flat semigroups
cites work: Flatness and amalgamation in semigroups
cites work: Q3848243
cites work: REPRESENTATION EXTENSION AND AMALGAMATION FOR SEMIGROUPS
cites work: Epimorphisms and dominions
cites work: Q3764354
cites work: Q3671388
description: scientific article; zbMATH DE number 4079761