On a generalization of principal weak flatness property.
type: Item
instance of: scholarly article
title: On a generalization of principal weak flatness property.
zbMATH Open document ID: 1258.20054
author: Husheng Qiao
author: Chongqing Wei
published in: Semigroup Forum
publication date: 2012-11-08T00:00:00Z
review text: The authors generalize principal weak flatness of acts to GP-flatness. A right \(S\)-act \(A\) is called GP-flat, if for every \(s\in S\), \(S\) a monoid, and any \(a,a'\in A\), \(a\otimes s=a'\otimes s\) in \(A\otimes S\) implies the existence of \(n\in\mathbb N\) such that \(a\otimes s^n=a'\otimes s^n\) in \(A\otimes Ss^n\). They show that GP-flat does not imply weakly flat. The concept is used to characterize so-called generally regular monoids, i.e. monoids \(S\) such that for every \(s\in S\) there exists \(n\in\mathbb N\) and \(x\in S\) such that \(s^n=sxs^n\).
reviewed by: Ulrich Knauer
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M30
zbMATH DE Number: 6103696
zbMATH Keywords: principally weak flatness
zbMATH Keywords: GP-flatness
zbMATH Keywords: right acts
zbMATH Keywords: monoids
MaRDI profile type: Publication
full work available at URL: s00233-012-9387-1
OpenAlex ID: W2053622534
cites work: Flat and strongly flat s-systems
cites work: Monoids over which all weakly flat acts are flat
cites work: PULLBACKS AND FLATNESS PROPERTIES OF ACTS. II
cites work: Eventually regular semigroups
cites work: Divisible S-systems and R-modules
cites work: Q4846425
cites work: Monoids, acts and categories. With applications to wreath products and graphs. A handbook for students and researchers
cites work: When torsion free acts are principally weakly flat
cites work: PULLBACKS AND FLATNESS PROPERTIES OF ACTS. I
cites work: Some new characterizations of right cancellative monoids by condition (PWP).
cites work: Q3408065
DOI: 10.1007/S00233-012-9387-1
description: scientific article; zbMATH DE number 6103696