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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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- Paul J. Allen, A fundamental theorem of homomorphism for semirings, Proc. Amer. Math. Soc., 21. (1969), 412-416.
- Shahabaddin Ebrahimi Atani, The ideal theory in quotients of commutative semirings, Glasnik Matematicki, 42. (62)(2007), 301-308.
- J. N. Chaudhari and D. R. Bonde, Ideal theory in quotient semirings, Thai J. Math., 12. (1) (2014), 95-101.
- J. N. Chaudhari, 2-absorbing ideals in semirings, Inter. J. Alg., 6(6)(2012), 265-270.
- J. N. Chaudhari and V. Gupta, Weak primary decomposition theorem for right Noetherian semirings, Indian J. Pure and Appl. Math, 25. (6)(1994), 647-654.
- L. Dale, Monic and monic free ideals in polynomial semiring, Proc. Am. Math. Soc., 56(1) (1976), 45-50.
- A. Y. Darani, On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative Semirings, Kyungpook Math. J., 52(2012), 91-97.
- J. S. Golan, Semirings and Their Applications, Kluwer, Dordrecht, 1999.
- Vishnu Gupta and J. N. Chaudhari, On partitioning ideals of semirings, Kyungpook Math. J., 46. (2006), 181-184.
- V. Gupta and J. N. Chaudhari, On prime ideals in semirings, Bull. Malaysian Math. Sc. Soc., 34(2) (2011), 417–421.
- T. K. Mukherjee, M. K. Sen and Shamik Ghosh, Chain Conditions on Semirings, Internat. J. Math. and Math. Sci., 19(2)(1996), 321-326.
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