On equalizer-flat and pullback-flat acts
type: Item
instance of: scholarly article
title: On equalizer-flat and pullback-flat acts
zbMATH Open document ID: 0625.20058
DOI: 10.1007/BF02575023
author: Peeter Normak
published in: Semigroup Forum
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/134903
review text: Let S be a monoid. A left S-act A is said to be equalizer-flat (pullback- flat) if the functor -\(\otimes A: Act\)-S\(\to Ens\) preserves equalizers (resp. pullbacks). Denote with (P) the following property of a left S-act A: if \(sa=tb\) for s,t\(\in S\) and a,b\(\in A\), then there are elements u,v\(\in S\) and \(a_ 1\in A\) such that \(su=tv\), \(ua_ 1=a\) and \(va_ 1=b\). It is shown that all equalizer-flat, pullback-flat acts or acts having property (P), are flat. All S-acts are pullback-flat (equalizer- flat) iff \(S=\{1\}\) \((S=\{1\}\) or \(S=\{0,1\})\). All S-acts have property (P) iff S is a group.
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 4015023
zbMATH Keywords: left S-act
zbMATH Keywords: equalizers
zbMATH Keywords: pullbacks
zbMATH Keywords: equalizer-flat
zbMATH Keywords: pullback-flat acts
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4015023