IDEALS IN SEMIRING WITH INVOLUTION

Abstract

In this paper, we study the notion of * -prime ideal in semiring with involution and shown that if M is a non-void * -m-system in a semiring with involution and if I is a * -ideal of R with I ∩ M = φ, then there exists a * -prime ideal P of R such that I ⊆ P and P ∩ M = φ.We also introduce the notion of * -k-prime ideal and we have shown that if P is a * -k-ideal of a semiring R with involution, then P is semiprime if and only if P is * -k-prime.