Principally Quasi-Injective Semimodules

Abstract

In this work, the notion of principally quasi- injective semimodule is introduced, discussing the conditions needed to get properties and characterizations similar or related to the case in modules. Let B be an R-semimodule with endomorphism semiring Ș. The semimodule B is called principally quasi-injective, if every R -homomorphism from any cyclic subsemimodule of B to B can be extended to an endomorphism of B.