Monoids over which all regular left acts are flat
type: Item
instance of: scholarly article
title: Monoids over which all regular left acts are flat
zbMATH Open document ID: 0827.20078
DOI: 10.1007/BF02573512
published in: Semigroup Forum
publication date: 1995-12-03T00:00:00Z
full work available at URL: https://eudml.org/doc/135374
review text: A left act over a monoid is said to be regular if all its cyclic subacts are projective. A left \(S\)-act \(B\) is called flat if the functor \(- \otimes B\) preserves all monomorphisms, and \(B\) is called (principally) weak flat if \(-\otimes B\) preserves embeddings of (principal) right ideals of \(S\) into \(S\). \(B\) is called faithful if for arbitrary \(s, t \in S\), \(b \in B\) from \(sb = tb\) it follows \(s = t\). In the paper a characterization of monoids over which all regular left \(S\)-acts are flat (weak flat, principally weak flat, faithful) is given. This is an answer to some questions remaining open in the article of \textit{M. Kil'p} and \textit{U. Knauer} [J. Pure Appl. Algebra 46, 217-231 (1987; Zbl 0619.20048)].
Mathematics Subject Classification ID: 20M50
zbMATH DE Number: 736949
zbMATH Keywords: left acts over monoids
zbMATH Keywords: cyclic subacts
zbMATH Keywords: embeddings
zbMATH Keywords: regular left \(S\)- acts
zbMATH Keywords: principally weak flat acts
zbMATH Keywords: faithful acts
author: Zhongkui Liu
reviewed by: Vladimir Fleischer
MaRDI profile type: Publication
cites work: Absolutely flat semigroups
cites work: Monoids over which all weakly flat acts are flat
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cites work: Q4126563
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description: scientific article; zbMATH DE number 736949