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2016•Indian Journal of Science and TechnologyOpen access

Quotient Seminear-Rings

Fawad Hussain

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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.Keywords: Seminear-ring, c-Ideals, Homomorphism, Congruence Relation, Quotient Seminear-Ring.

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What this paper is about

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.Keywords: Seminear-ring, c-Ideals, Homomorphism, Congruence Relation, Quotient Seminear-Ring.

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Available 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.Keywords: Seminear-ring, c-Ideals, Homomorphism, Congruence Relation, Quotient Seminear-Ring.

Key concepts: Quotient, Homomorphism, Mathematics, Semiring, Congruence relation, Quotient ring, Congruence (geometry), Pure mathematics

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