Bi-quasi Ideals and Fuzzy Bi-quasi Ideals of Semigroups
Abstract
In this paper,as a further generalization of ideals, we introduce the notion of bi-quasi ideal of Г- semigroup as a generalization of bi-ideal of Г-semigroup. We study the properties of bi-quasi ideal, characterize the bi-quasi simple Г-semigroup andregular Г-semigroup using bi-quasi ideals. We introduce the notion of fuzzy bi-quasi ideal of Г-semigroup as a generalization of fuzzy bi-ideal and we characterize the regular Г-semigroup in terms of fuzzy bi-quasi ideals of Г-semigroup.
References
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[13] M. K. Sen. On Г-semigroup, Proc. of International Conference of algebra and its application, (pp. 301–308.) Decker Publicaiton, New York, 1981.
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[2] K. Iseki. Quasi-ideals in semirings without zero, Proc. Japan Acad., 34 (1958), 79-84.
[3] N. Kuroki. On fuzzy semigroups, Information Sciences, 53(3) (1991), 203–236.
[4] S. Lajos. On the bi-ideals in semigroups, Proc. Japan Acad., 45(1969), 710-712.
[5] S. Lajos and F. A. Szasz. On the bi-ideals in associative ring, Proc. Japan Acad., 46 (1970), 505-507.
[6] H. Lehmer. A ternary analogue of abelian groups, Amer. J. Math., 59 (1932) 329–338.
[7] W. J. Liu. Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and Systems, 8 (2) (1982), 133–139.
[8] W. G. Lister. Ternary rings, Tran. of American Math. Society, 154 (1971), 37–55.
[9] D. Mandal. Fuzzy ideals and fuzzy interior ideals in ordered semirings, Fuzzy info. and Engg., 6 (2014), 101–114.
[10] M. Murali Krishna Rao. Г-semirings-I, Southeast Asian Bull. Math., 19 (1)(1995), 49–54.
[11] N. Nobusawa. On a generalization of the ring theory, Osaka. J. Math., 1 (1964), 81 – 89.
[12] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35(1971), 512-517.
[13] M. K. Sen. On Г-semigroup, Proc. of International Conference of algebra and its application, (pp. 301–308.) Decker Publicaiton, New York, 1981.
[14] O. Steinfeld. Uher die quasi ideals, Publ. Math., Debrecen, 4(1956), 262 - 275.
[15] U. M. Swamy and K. L. N. Swamy. Fuzzy prime ideals of rings, Jour. Math. Anal. Appl., 134 (1988), 94–103.
[16] L. A. Zadeh. Fuzzy sets, Information and control, 8 (1965), 338–353.
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2016-12-27
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