Flatness properties of monocyclic acts
type: Item
instance of: scholarly article
title: Flatness properties of monocyclic acts
zbMATH Open document ID: 0862.20050
DOI: 10.1007/BF01326031
author: Sydney Bulman-Fleming
author: Peeter Normak
published in: Monatshefte für Mathematik
publication date: 1997-01-14T00:00:00Z
full work available at URL: https://eudml.org/doc/178749
review text: Let \(S\) be a monoid, \(\rho(s,t)\) is the smallest right congruence on \(S\) identifying the elements \(s\) and \(t\) of \(S\). Then \(S/\rho(s,t)\) is a right \(S\)-act and such acts are called monocyclic. Results of the following kind are contained in the paper. All projective monocyclic right \(S\)-acts are free if and only if all projective right \(S\)-acts are free, i.e. if and only if \(e{\mathcal D}1\) for all \(e^2=e\in S\). All possible combinations of these types or statements are presented where ``projective'' or ``free'' are replaced by ``strongly flat'', ``\((P)\)'', ``flat'', ``weakly flat'', ``principally weakly flat'', ``torsion free'' and, at the first place in the above statement, also ``all''. The possible 36 results are either proved or cited in the paper.
reviewed by: Ulrich Knauer
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M10
zbMATH DE Number: 955268
zbMATH Keywords: right congruences
zbMATH Keywords: projective monocyclic right \(S\)-acts
zbMATH Keywords: projective right \(S\)-acts
MaRDI profile type: Publication
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OpenAlex ID: W2032789586
description: scientific article; zbMATH DE number 955268