An approach to injective acts over monoids based on indecomposability
Mojtaba Sedaghatjoo, Mohammad Ali Naghipoor · Communications in Algebra · 2016
The main purpose of this paper is to investigate classes of acts that are injective relative to all embeddings with indecomposable domains or codomains. We give some homological classifications of monoids in light of such kinds of injectivity. Our approach to the indecomposability property provides a new characterization of right absolutely injective monoids such that all indecomposable acts are injective.