Fuzzy Prime Ideals in Ordered Г-Semirings


  • Marapureddy Murali Krishna Rao


We introduce the notion of ideal, prime ideal, fuzzy ideal, fuzzy
prime ideal of ordered Г -semiring and study their properties and relations between them. We characterize the prime ideals of ordered Г - semiring with respect to fuzzy ideals. And also characterize simple ordered Г - semiring with respect to fuzzy prime ideals of ordered We introduce the notion of ideal, prime ideal, fuzzy ideal, fuzzy


[1] T. K. Dutta, S. K. Sardar and S. Goswami. Operations on fuzzy ideals of Г -semirings, arXiv:1101.4791 [math.RA], 25 Jan 2011.

[2] Y. B. Jun and C. Y. Lee. Fuzzy Г '- rings, Pusan Kyongnam Math. J. (now, emphEast Asian Math. J.) 8(2)(1992), 163-170.

[3] Y. B. Jun, J. Naggers and H. S. Kim. Normal L-fuzzy ideal in semirings, Fuzzy Sets and Systems, 82(3)(1996), 383-386.

[4] N. Kuroki. On fuzzy semigroups, Information Sciences, 53(3)(1991), 203-236.

[5] H. Lehmer. A ternary analogue of abelian groups, American J. Math., 59(2)(1932), 329-338.

[6] W. J. Liu. Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8(2)(1982), 133-139.

[7] W. G. Lister. Ternary rings, Tran. Amer. Math. Soc., 54 (1971), 37-55.

[8] D. Mandal. Fuzzy ideals and fuzzy interior ideals in ordered semirings, Fuzzy Inf. Eng., 6(1)(2014), 101-114.

[9] M. Murali Krishna Rao. Г - semirings-I, Southeast Asian Bull. Math., 19(1)(1995), 49-54.

[10] M. Murali Krishna Rao. Г - semirings-II, Southeast Asian Bull. Math., 211997, 281-287.

[11] M. Murali Krishna Rao. The Jacobson Radical of a Г - semiring, Southeast Asian Bull. Math., 23(1)(1999), 127-134.

[12] M. Murali Krishna Rao. T-fuzzy ideals in ordered Г - semirings, Ann. Fuzzy Math. Informatics, 13(2)(2017), 8-31.

[13] M. Murali Krishna Rao. Fuzzy soft Г - semiring and fuzzy soft k ideal over Г - semiring, Ann. Fuzzy Math. Informatics, 9(2)(2015), 341-354.

[14] M. Murali Krishna Rao and B. Venkateswarlu. Fuzzy Фиlters in Г - semirings, Malaya J. Mat., 3(1)(2015), 93-98.

[15] M. Murali Krishna Rao and B. Venkateswarlu. Regular Г - semiring and Фиeld Г - semiring, Novi Sad J. Math., 45 (2) (2015), 155-171.

[16] N. Nobusawa. On a generalization of the ring theory, Osaka. J. Math., 1(1)(1964), 81-89.

[17] A. Rosenfeld. Fuzzy groups, J. Math.Anal.Appl., 5(3)(1971), 512-517.

[18] M. K. Sen. On Г - semigroup, Procedings of the International Conference of Algebra and its Application, (pp. 301{308) , Decker Publicaiton, New York, 1981.

[19] U. M. Swamy and K. L. N. Swamy. Fuzzy prime ideals of rings, J. Math. Anal. Appl., 134(1)(1988), 94-103.

[20] H. S. Vandiver. Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc. (N.S.), 40(12)(1934), 914-920.

[21] L. A. Zadeh. Fuzzy sets, Information and Control, 8(3)(1965), 338-353.

[22] Y. Zhang. Prime L-fuzzy ideals and primary L-fuzzy ideals, Fuzzy Sets and Systems, 27(3)(1988), 345-350.