Flatness properties of diagonal acts over monoids.
type: Item
instance of: scholarly article
title: Flatness properties of diagonal acts over monoids.
zbMATH Open document ID: 1183.20065
author: Sydney Bulman-Fleming
author: Andrew Gilmour
published in: Semigroup Forum
publication date: 2009-10-14T00:00:00Z
review text: Let \(S\) be a monoid. The right \(S\)-act \(S\times S\), denoted by \(D(S)\), equipped with componentwise \(S\)-action, is called the diagonal act of \(S\). In this paper, some kinds of flatness properties for \(D(S)\) are discussed. Conditions (including some sufficient and necessary conditions) for \(D(S)\) to be principally weakly flat, weakly flat, flat, strongly flat, and satisfying condition (P), condition (E) are obtained in succession. Characterizations of projective, free, flat, and other diagonal acts of some special kinds of semigroups, such as right cancellative monoids, commutative monoids, and complete simple semigroups, complete 0-simple semigroups, are studied simultaneously.
reviewed by: Chen Yuqun
Mathematics Subject Classification ID: 20M50
zbMATH DE Number: 5614944
zbMATH Keywords: diagonal acts
zbMATH Keywords: flat acts
zbMATH Keywords: monoids
zbMATH Keywords: finitely generated acts
zbMATH Keywords: flatness
zbMATH Keywords: projective right acts
MaRDI profile type: Publication
full work available at URL: s00233-009-9144-2
OpenAlex ID: W2076116808
cites work: On the Finite and Nonfinite Generation of Diagonal Acts
cites work: Monoids, acts and categories. With applications to wreath products and graphs. A handbook for students and researchers
cites work: Q4846425
cites work: Monoids over which all weakly flat acts are flat
cites work: Q5564342
cites work: On equalizer-flat and pullback-flat acts
cites work: Pullback-Flat Acts are Strongly Flat
cites work: Q4022827
cites work: Products of projective S-Systems
cites work: Q4771385
DOI: 10.1007/S00233-009-9144-2
description: scientific article; zbMATH DE number 5614944