A Study of r-Ideals, K-Ideals and m−k Ideals of Ordered Semirings

Abstract

A. In this paper, we introduce the notion of k-ideal, r-ideal and m-k ideal in ordered semirings. We study the properties of ideals in ordered semirings, the relations between them and characterize m-k ideals using derivation of ordered semirings. We prove that if I is a maximal ideal of an ordered semiring M with unity satisfying a + b = 1, for all a, b ∈ M then I is a m-k ideal of M.