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On B-Ideals in Semirings


Affiliations
1 Department of Mathematics, ACS College, Dharangaon 425 105,, India
2 Department of Mathematics, M. J. College, Jalgaon 425002, India
     

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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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  • On B-Ideals in Semirings

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Authors

Dipak Ravindra Bonde
Department of Mathematics, ACS College, Dharangaon 425 105,, India
Jayprakash Ninu Chaudhari
Department of Mathematics, M. J. College, Jalgaon 425002, India

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.

Keywords


Semiring, Zerosumfree Semiring, Subtractive Ideal, Partitioning Ideal, B-ideal, Strong B-ideal, Quotient Semiring, K-Noetherian Semiring, Polynomial Semiring, Monic Ideal, Coefficient Ideal.

References





DOI: https://doi.org/10.18311/jims%2F2020%2F24429