Generalization of Quasi Principally Injective S-Acts

The purpose of this paper is to introduce a new kind of generalization of quasi principally injective S-acts over monoids (QP-injective), (and hence generalized quasi injective), namely quasi small principally injective S-acts. Several properties of this kind of generalization are discussed. Some of these properties are analogous to that notion of quasi small principally injective for general modules. Characterizations of quasi small principally injective acts are considered. Conditions are investigated under which subacts are inheriting quasi small principally injective property. Citation: Shaymaa Amer Abdul-Kareem. "Generalization of Quasi Principally Injective S-Acts." Global Research and Development Journal For Engineering 4.3 (2019): 1 - 4.