(untitled) (JOURNAL OF UNIVERSITY OF BABYLON for Pure and Applied Sciences, 2019)
In this paper, the connotation principally pseudo-injective semimodule which is a generalization of the notion principally quasi-injective semimodule will be introduced, we study some properties of principally pseudo-injective semimodule. Relationship between principally pseudo-injective and principally quasi-injective semimodule is given. A semimodule is called principally pseudo-injective (shortly, P.P.-injective) if for any cyclic subsemimodule Ų of, any monomorphism from Ų into can be extended to an endomorphism of.