Weak projectives of finite semigroups
type: Item
instance of: scholarly article
title: Weak projectives of finite semigroups
zbMATH Open document ID: 1030.20044
DOI: 10.1016/S0021-8693(03)00278-3
author: Yevhen Zelenyuk
published in: Journal of Algebra
publication date: 2003-08-20T00:00:00Z
review text: Let \(\mathcal P\) be a collection of finite bands of certain type, let \(\mathcal F\) be the category of finite semigroups and \(\mathcal C\) the category of compact right topological semigroups. An algebra is called `weak projective' if it is projective with respect to surjective epimorphisms. The main theorem proves equivalence of eight statements for a finite semigroup \(S\) including the following: (1) \(S\) is isomorphic to some semigroup of \(\mathcal P\); (2) \(S\) is a weak projective in \(\mathcal F\); (3) \(S\) is a weak projective in \(\mathcal C\).
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20A15
zbMATH DE Number: 1967899
zbMATH Keywords: weak projectives
zbMATH Keywords: absolute coretracts
zbMATH Keywords: finite semigroups
zbMATH Keywords: compact right topological semigroups
zbMATH Keywords: finite bands
reviewed by: Peeter Normak
MaRDI profile type: Publication
cites work: Algebra in the Stone-Čech compactification: theory and applications
cites work: Q3853827
cites work: Q3708991
cites work: Projectives of finite regular semigroups
cites work: Topological groups with finite semigroups of ultrafilters
cites work: On topological groups with finite ultrafilter semigroups
cites work: Finite groups in \(\beta\mathbb{N}\) are trivial
cites work: On subsemigroups of \(\beta\mathbb{N}\) and absolute coretracts
description: scientific article; zbMATH DE number 1967899