An Approach to Injective Acts over Monoids Based on Indecomposability
Mojtaba Sedaghatjoo, Mohammad Ali Naghipoor
TL;DR
This paper explores injective acts over monoids focusing on indecomposable acts, providing new characterizations of right absolutely injective monoids through homological classifications.
Contribution
It introduces a novel approach to indecomposability, offering a new characterization of right absolutely injective monoids based on injectivity of indecomposable acts.
Findings
Characterization of right absolutely injective monoids via indecomposable acts
Homological classifications of monoids related to injectivity
New criteria for injectivity in monoid acts
Abstract
The main purpose of this paper is investigating 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 indecomposable property provides a new characterization of right absolutely injective monoids as ones that all indecomposable acts are injective.
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