Hereditary torsion theory of pseudo-regular \(S\)-systems
type: Item
instance of: scholarly article
title: Hereditary torsion theory of pseudo-regular \(S\)-systems
zbMATH Open document ID: 1020.20040
author: Derong Qiu
published in: Semigroup Forum
publication date: 2003-03-18T00:00:00Z
review text: Let \(S\) be a semigroup with 0 and 1, and let \(M\) be a right \(S\)-system. An element \(m\in M\) is called `pseudo-regular' if there exists an element \(s\not=1\) such that \(m\cdot s=m\); \(M\) is called `pseudo-regular' if all its elements are pseudo-regular. The author develops a torsion theory \(\tau_u=(U_S,\overline U_S)\) with its torsion class \(U_S\) consisting of all pseudo-regular \(S\)-systems (and \(\overline U_S\) consisting of all right \(S\)-systems with no non-zero pseudo-regular \(S\)-subsystems). For a pseudo-regular torsion theory, the structure of the corresponding quasi-filter is described. A torsion theory \((\mathcal{T,F})\) is called `stable' if \(\mathcal T\) is closed under injective hulls. The article finds conditions for a monoid \(S\) under which the torsion theory \(\tau_u=(U_S,\overline U_S)\) is stable. The special case of 0-right simple semigroups is considered.
reviewed by: Peeter Normak
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 1883945
zbMATH Keywords: pseudo-regular \(S\)-systems
zbMATH Keywords: hereditary torsion theories
zbMATH Keywords: quasi-filters
zbMATH Keywords: stable torsion theories
zbMATH Keywords: injective hulls
MaRDI profile type: Publication
full work available at URL: s002330010147
OpenAlex ID: W2057245927
DOI: 10.1007/S002330010147
description: scientific article; zbMATH DE number 1883945