Subtractive Extension of Ideals in Ternary Semirings

Jayprakash Ninu Chaudhari, Kunal Julal Ingale

Abstract

In this paper, we introduce the concept of subtractive extension of an
ideal of a ternary semiring. Further 1) A characterization of subtractive extensions of ideals in the ternary semiring of non-positive integers is investigated. 2) The relation between subtractive extensions of a Q-ideal I in a ternary semiring S and the ideals in the quotient ternary semiring S/I(Q) is obtained. 3) We show that a subtractive extension P of a Q-ideal I in a ternary semiring S is a prime (semiprime) ideal if and only if P/I(Q P) is a prime (semiprime) ideal in the quotient ternary semiring S/I(Q).