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CHARACTERIZATION OF REGULAR $\Gamma$−SEMIGROUPS THROUGH FUZZY IDEALS | ||
| Iranian Journal of Fuzzy Systems | ||
| مقاله 6، دوره 4، شماره 2، دی 2007، صفحه 57-68 اصل مقاله (192.05 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22111/ijfs.2007.375 | ||
| نویسندگان | ||
| P. Dheena1؛ S. Coumaressane* 2 | ||
| 1Department of Mathematics, Annamalai University, Annamalainagar- 608002, India | ||
| 2Department of Mathematics,Annamalai University, Annamalainagar- 608002, India | ||
| چکیده | ||
| Notions of strongly regular, regular and left(right) regular $\Gamma$−semigroups are introduced. Equivalent conditions are obtained through fuzzy notion for a $\Gamma$−semigroup to be either strongly regular or regular or left regular. | ||
| کلیدواژهها | ||
| $\Gamma$−semigroup؛ Bi-ideal؛ Quasi-ideal؛ Regular؛ Strongly regular؛ Left(right) regular؛ Fuzzy (left؛ right)ideal؛ Fuzzy quasi-ideal؛ Fuzzy bi-ideal | ||
| مراجع | ||
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[1] P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84 (1981), 264-269. [2] Y. I. Kwon and S. K. Lee, The weakly semi-prime ideals of po−$\Gamma$−semigroups, Kangweon- Kyungki Math. J., 5 (1997), 135-139. [3] Y. I. Kwon and S. K. Lee, On the left regular po−$\Gamma$−semigroups, Kangweon-Kyungki Math. J., 6 (1998), 149-154. [4] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982), 133-139. [5] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517. [6] N. K. Saha, On $\Gamma$−semigroup II, Bull. Cal. Math. Soc., 79 (1987), 331-335. [7] M. K. Sen, On $\Gamma$−semigroups, Proc. of the Int. Conf. on Algebra and it’s Appl., Decker Publication, New York 301 (1981). [8] M. K. Sen and N. K. Saha, On $\Gamma$−semigroup I, Bull. Cal. Math. Soc., 78 (1986), 180-186. [9] L. A. Zadeh, Fuzzy sets, Inform. and Control, 8 (1965), 338-353. | ||
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