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 be an -semimodule with endomorphism semiring Ș. The semimodule is called principally quasi-injective, if every -homomorphism from any cyclic subsemimodule of to can be extended to an endomorphism of .