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