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On B-Ideals in Semirings
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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.
Keywords
Semiring, Zerosumfree Semiring, Subtractive Ideal, Partitioning Ideal, B-ideal, Strong B-ideal, Quotient Semiring, K-Noetherian Semiring, Polynomial Semiring, Monic Ideal, Coefficient Ideal.
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