Derivation in ternary semiring

Abstract

The purpose of this paper is to introduce the notion of derivation, differential ideal, differential k-ideal (differential h-ideal) in ternary semiring and to study the validity of some of the results on prime ideals and prime radicals of ternary semirings replacing ideals by differential ideals, radicals by differential radicals, ternary semirings by differential ternary semirings.Among others we deduce that a radical differential ideal I in a differential ternary semiring is the intersection of all prime differential ideals containing I. Also we deduce that in a differential ternary semiring satisfying ascending chain condition on radical differential ideals any radical differential ideal is expressible as the intersection of finite number of differential ideals.