Fuzzy Bi-ideals in Ternary Semirings
Commenced in January 2007
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Fuzzy Bi-ideals in Ternary Semirings

Authors: Kavikumar, Azme Khamis, Young Bae Jun,

Abstract:

The purpose of the present paper is to study the concept of fuzzy bi-ideals in ternary semirings. We give some characterizations of fuzzy bi-ideals. Characterizations of regular ternary semirings are provided.

Keywords: Fuzzy ternary subsemiring, fuzzy quasi-ideal, fuzzy bi-ideal, regular ternary semiring

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1334744

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[1] T. K. Dutta, S. Kar, On Regular Ternary Semirings, Advances in Algebra, proceedings of the ICM Satellite Conference in Algebra and Related Topics, World Scientific, New Jersey (2003) 343-355.
[2] T. K. Dutta, S. Kar, A Note on Regular Ternary Semirings, KYUNGPOOK Math. Journal 46 (2006), 357-365.
[3] R. A. Good, D. R. Hughes, Associated Groups for a Semigroup, Bulletin of American Mathematical Society, 58 (1952), 624-625.
[4] Y. B. Jun, J. Neggers, H. S. Kim, On L-fuzzy ideals in semiringd I, Czechoslovak Math. Journal, 48 (123) (1998) 669-675.
[5] S. Kar, On Quasi-ideals and Bi-ideals in Ternary Semirings, Internarional Journal ofMathematics andMathematical Sciences 2005:18 (2005) 3015-3023.
[6] J. Kavikumar, Azme Bin Khamis, Fuzzy ideals and Fuzzy Quasi-ideals of Ternary Semirings, IAENG International Journal of AppliedMathematics, 37: 2 (2007) 102-106.
[7] C. B. Kim, Mi-Ae Park, k-Fuzzy ideals in Semirings, Fuzzy Sets and Systems 81 (1996) 281-286.
[8] D. H. Lehmer, A Ternary Analogue of Abelian Groups, American Journal of Mathematics, 59 (1932) 329-338.
[9] W. G. Lister, Ternary Rings, Transaction of American Mathematical Society, 154 (1971) 37-55.
[10] W. Liu, Fuzzy invariant subgroups and Fuzzy ideals, Fuzzy Sets and Systems, 8 (1982) 133-139.
[11] O. Steinfeld, ¨Uber die Quasiideale von Halbgruppen, Publ. Math. Debrecen 4 (1956) 262-275 (German).
[12] O. Steinfeld, ¨Uber die Quasiideale von Ringen, Acta Science Math. (Szeged) 17 (1956) 170-180 (German).
[13] A. Rosenfeld, Fuzzy Groups, Journal of Mathematical Analysis and Applications, 35 (3) (1971) 512-517.
[14] L. A. Zadeh, Fuzzy Sets, Information and Control, 8 (3) (1965) 338-353.