On relatively injective and weakly injective \(S\)-acts
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].
scientific article; zbMATH DE number 1267311