In this paper we study the relationship between Essentially Small Quasi-Dedekind modules and anti-hopfian modules. Also, we give some examples which illustrate these relations.

In this work, the notion of semi-injectivity of systems has been introduced and studied, which is a generalization of quasi-injectivity. We obtain a characterization of semi-injectivity analogous to that of quasiinjectivity. Certain class of subsystems which inheret this property have been considered. Finally, we studied the linear equation systems on this kind of injectivity.

In this work, we present and investigate the class of acts that are strongly extending relative to -reversible subacts in the category of S-acts with zero element. Many characterizations and properties of -reversible extending acts are described. Many results which are known for strongly uniform extending modules and strongly uniform continuous modules are generalized to S-acts with zero element.