Indian Journal of Science and Technology
Year: 2016, Volume: 9, Issue: 38, Pages: 1-7
Fawad Hussain1 , Muhammad Tahir2 , Saleem Abdullah2 and Nazia Sadiq2
1 Department of Mathematics, Abbottabad University of Science and Technology, Pakistan; [email protected]
2 Department of Mathematics, Hazara University Mansehra, Pakistan; [email protected]
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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