Endomorphism Semirings of Dedekind Semimodules

Abstract

The aim of this paper is to study the concept of a semiring of endomorphisms of a

(Dedekind) semimodules (or simply semimodules).Here we prove that wheneveris asemimodule thenevery non-zero element ofis a monomorphism,and sois entire semiring. In this paper we prove that ifis an ideal of a semiringthen under some conditions we get is commutative semiring. This  paper  is  devoted  to prove wheneveris a dualizablesemimodule over a semiringand under certain condition thenis commutative entire semiring.

 Keywords: Dedekind semimodule, Entire semiring, Invertible subsemimodule, Semidomain.