On B-Ideals in Semirings

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Authors

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

DOI:

https://doi.org/10.18311/jims/2020/24429

Keywords:

Semiring, Zerosumfree semiring, Subtractive ideal, Partitioning ideal, B-ideal, Strong B-ideal, Quotient semiring, k-Noetherian semiring, Polynomial semiring, Monic ideal, Coefficient ideal.

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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Published

2020-05-15

How to Cite

Ravindra Bonde, D., & Ninu Chaudhari, J. (2020). On <i>B</i>-Ideals in Semirings. The Journal of the Indian Mathematical Society, 87(1-2), 1–8. https://doi.org/10.18311/jims/2020/24429

Issue

Volume 87, Issue 1-2, January-June 2020

Section

Articles

License

Copyright (c) 2020 Dipak Ravindra Bonde, Jayprakash Ninu Chaudhari

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

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Europe PMC
Received 2019-11-11
Accepted 2023-01-30
Published 2020-05-15

 

References

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