2020•Journal of the Indian Mathematical SocietyOpen access

On B-Ideals in Semirings

Dipak Ravindra Bonde, Jayprakash Ninu Chaudhari

Abstract

In this paper, we introduce the notion of B-ideal in a commutative semiring R. Then 1) A characterization of B-ideals in the Semiring of non-negative integers is obtained. 2) Relation between B-ideals in a semiring R containing a Q-ideal I of R and B-ideals in the quotient semiring R/I(Q) is obtained. Further study of k-Noetherian semirings is developed. Also B-ideals in polynomial semirings are studied.

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Key concepts: Semiring, Mathematics, Ideal (ethics), Quotient, Noetherian, Combinatorics, Algebra over a field, Pure mathematics