On Fuzzy Weakly Completely Prime Ideal in Γ -Semigroups

Year 2010, Volume: 5 Issue: 2, 230 - 238, 11.11.2010

Samit Majumder

Abstract

In this paper the notion of fuzzy weakly completely prime ideal in Γ -semigroups has been introduced. Finally, the concept of operator semigroups of a Γ -semigroup has been employed to study the relationship between their respective fuzzy weakly completely prime ideals.

Keywords

Γ -semigroup, Operator semigroups, Fuzzy subsemigroup, Fuzzy weakly completely prime ideal

Γ -Yarıgruplarda Bulanık Zayıf Tam Asal İdeal Üzerine

Abstract

Bu çalışmada, Γ -yarıgruplarda bulanık zayıf tam asal ideal kavramı verilmiştir. Bir Γ -yarıgrubunun operator yarıgrupları kavramı, bunların temsili bulanık zayıf tam asal idealleri arasındaki ilişkiler ortaya konulmuştur

Keywords

Γ -yarıgrup, Operatör yarıgruplar, Bulanık altyarıgruplar, Bulanık zayıf tam asal ideal.

References

• [1] Howie J.M., 1995. Fundamentals of semigroup theory, London Mathematical Society Monographs. New Series, 12. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York. p.319.
• [2] Sen M.K., 1981. On Γ -semigroups, Proceedings of the International conference on Algebra and its application. Decker Publication, New York, p.301.
• [3] Sen M.K., Saha N.K, 1986. On Γ -semigroups I, Bulletin of Calcutta Mathematical Society, 78, 180-186.
• [4] Saha N.K., 1987. On Γ -semigroup II, Bulletin of Calcutta Mathematical Society, 79, 331-335.
• [5] Chattopadhyay S., 2001. Right inverse Γ -semigroup. Bulletin of Calcutta Mathematical Society, 93, 435- 442.
• [6] Chattopadhyay S., 2005. Right orthodox Γ -semigroup, Southeast Asian Bulletin of Mathematics, 29, 23- 30.
• [7] Dutta T.K., Adhikari N.C., 1993. On Γ -semigroup with the right and left unities, Soochow Journal of Mathematics, 19 (4): 461-474.
• [8] Dutta T.K., Adhikari N.C., 1994. On prime radical of Γ -semigroup, Bulletin of Calcutta Mathematical Society, 86 (5): 437-444.
• [9] Hila K., 2008. On regular, semiprime and quasi-reflexive Γ -semigroup and minimal quasiideals, Lobachevskii Journal of Mathematics, 29, 141-152.
• [10] Hila K., 2007. On some classes of le-Γ -semigroup, Algebras, Groups and Geometries, 24, 485-495.
• [11] Chinram R., 2006. On quasi-Γ -ideals in Γ -semigroup, Science Asia, 32, 351-353.
• [12] Seth A., 1992. Γ -group congruences on regular Γ -semigroups, International Journal of Mathematics and Mathematical Sciences, 15 (1): 103-106.
• [13] Zadeh L.A., 1965. Fuzzy Sets, Information and Control, 8, 338-353.
• [14] Kuroki N., 2004. Fuzzy semiprime ideals in semigroups, Fuzzy Sets and Systems, 158, 277-288.
• [15] Kuroki N., 1991. On fuzzy semigroups, Information Sciences, 53 (3): 203-236.
• [16] Kuroki N., 1981. On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems, 5, 203- 215.
• [17] Uckun M., Öztürk M.A., Jun Y.B., 2007. Intuitionistic fuzzy sets in gamma-semigroups, Bulletin of Korean Mathematical Society, 44(2) 359-367.
• [18] Sardar S.K., Majumder S.K., 2009. On fuzzy ideals in Γ -semigroup, International Journal of Algebra, 3 (16): 775-784.
• [19] Sardar S.K., Majumder S.K., Mandal D., 2009. A note on characterization of prime ideals of Γ -semigroups in terms of fuzzy subsets, International Journal of Contemporary Mathematical Sciences., 4 (30) 1465-1472.
• [20] Dutta T.K., Sardar S.K., Majumder S.K., 2009. Fuzzy ideal extensions of Γ -semigroups via its operator semigroups, International Journal of Contemporary Mathematical Sciences, 4 (30): 1455-1463.
• [21] Dutta T.K., Sardar S.K., Majumder S.K., 2009. Fuzzy ideal extensions of Γ -semigroups, International Mathematical Forum, 4 (42): 2093-2100.
• [22] Kim J., 2009. Some fuzzy semiprime ideals in semigroups, Journal of Chungcheong Mathematical Society, 3(22): 277-288.