Quotient seminear-rings

Abstract

The study of a seminear-ring was started in 1967. Seminear-ring is the generalization of semiring and nearing. It is known that in a semiring the quotient structure is constructed by congruence relations through c-ideals and homomorphisms. We apply the said congruence relations to a seminear-ring and get quotient structure of a seminear-ring. The aim of this paper is to discuss quotient seminear-rings in two different ways. We study congruence relations, homomorphisms and ideals. We show that each homomorphism and c-ideal define a congruence relation on seminear-rings. At the end, we discuss quotient seminear-rings.