On relatively injective and weakly injective \(S\)-acts
type: Item
instance of: scholarly article
title: On relatively injective and weakly injective \(S\)-acts
zbMATH Open document ID: 0921.20055
published in: Southeast Asian Bulletin of Mathematics
publication date: 1999-08-05T00:00:00Z
review text: Let \(S\) be a monoid. The article is devoted to the study of some generalizations of injectivity (P-injectivity, F-injectivity, finite injectivity) in the category of right \(S\)-acts. For example, for a commutative monoid \(S\), every PQI \(S\)-act is P-injective if and only if \(S\) is regular (an \(S\)-act is called P-injective if it is injective relative to monomorphisms of principal right ideals into \(S\); an act \(M\) is called PQI if any homomorphism of a P-injective subact of \(M\) into \(M\) can be extended to an endomorphism of \(M\)). The whole list of results about finitely injective acts presented in the paper coincides literally with that published by the reviewer [in Proceedings of the conference ``Methods of Algebra and Analysis'', p. 22-23, held in Tartu, Sept. 1988].
Mathematics Subject Classification ID: 20M50
zbMATH DE Number: 1267311
zbMATH Keywords: P-injective acts
zbMATH Keywords: F-injective acts
zbMATH Keywords: finitely injective acts
zbMATH Keywords: generalizations of injectivity
zbMATH Keywords: categories of acts
author: Javed Ahsan
author: Zhongkui Liu
reviewed by: Peeter Normak
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1267311