On free, projective, and strongly flat acts
type: Item
instance of: scholarly article
title: On free, projective, and strongly flat acts
zbMATH Open document ID: 0588.20041
DOI: 10.1007/BF01202495
author: Mati Kilp
author: Ulrich Knauer
published in: Archiv der Mathematik
publication date: 1986-01-01T00:00:00Z
review text: The homological classification of monoids is considered. Theorem: All flat left S-acts (injective cogenerators, all cofree, all injective left S-acts) are strongly flat iff \(S=\{1\}\). Theorem: All projective generators in S-Act are free iff any eS, \(e^ 2=e\in S\), containing a left invertible element can be generated by a left invertible element. All terms have their usual categorical meaning, a left S-act M is called strongly flat if tensoring by M preserves equalizers and pullbacks.
Mathematics Subject Classification ID: 20M50
Mathematics Subject Classification ID: 20M10
Mathematics Subject Classification ID: 18B40
Mathematics Subject Classification ID: 68Q70
zbMATH DE Number: 3944157
zbMATH Keywords: monoids
zbMATH Keywords: flat left S-acts
zbMATH Keywords: injective cogenerators
zbMATH Keywords: injective left S-acts
zbMATH Keywords: strongly flat
zbMATH Keywords: projective generators
zbMATH Keywords: left invertible element
MaRDI profile type: Publication
cites work: The Injective Envelope of S-Sets
cites work: Indecomposable and Injective S‐systems with Zero
cites work: Perfect semigroups
cites work: Projectivity of acts and Morita equivalence of monoids
cites work: Q3314059
cites work: Characterization of monoids by torsion-free, flat, projective, and free acts
cites work: Q4123496
full work available at URL: https://doi.org/10.1007/bf01202495
OpenAlex ID: W2051030855
description: scientific article; zbMATH DE number 3944157