On Prime and Maximal k-Subsemimodules of Semimodules

Abstract

In this paper, we present some characterizations of prime k-ideals andmaximal k-ideals of a semiring. Then we extend these properties toprime k-subsemimodules and maximal k-subsemimodules of a semimodule. After that, the correspondence between prime k-ideals andprime k-subsemimodules, and between maximal k-ideals and maximalk-subsemimodules are given.