Principally pseudo-injective semimodule

الملخص EN

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 Ųof , any monomorphism from Ų into can be extended to endomorphism of .