FUZZY 2-(0-OR 1-)PRIME IDEALS IN SEMIRINGS

Title & Authors
FUZZY 2-(0-OR 1-)PRIME IDEALS IN SEMIRINGS
Dheena, P.; Coumaressane, S.;

Abstract
In this Paper three different types of fuzzy Prime ideals are introduced. Condition is obtained for a fuzzy 2-prime ideal will have two elements in its range. It has been shown that A is fuzzy 2-prime ideal of the semiring R if and only if 1-A is a fuzzy $\small{m_2-system}$ in R.
Keywords
semiring;fuzzy ideal;fuzzy point;fuzzy 2-(0-or 1-) prime ideal;fuzzy $\small{m_2(m_0\;or\;m_1)-system}$;
Language
English
Cited by
1.
ON FUZZY k−IDEALS, k−FUZZY IDEALS AND FUZZY 2−PRIME IDEALS IN Γ−SEMIRINGS,;;

Journal of applied mathematics & informatics, 2016. vol.34. 5_6, pp.405-419
1.
Fuzzy ideals of semirings, Neural Computing and Applications, 2011, 20, 8, 1219
2.
ON FUZZY k−IDEALS, k−FUZZY IDEALS AND FUZZY 2−PRIME IDEALS IN Γ−SEMIRINGS, Journal of applied mathematics & informatics, 2016, 34, 5_6, 405
3.
Proper Fuzzification of Prime Ideals of a Hemiring, Advances in Fuzzy Systems, 2012, 2012, 1
References
1.
S. Abou-Zaid, On fuzzy subnear-rings and ideals, Fuzzy Sets and Systems, 44 (1991), no. 1, 139-146

2.
S. I. Baik and H. S. Kim, On fuzzy k-ideals in semirings, Kangweon-Kyungki Math. Jour. 8 (2000), 147-154

3.
P. Sivaramakrishna Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 84 (1981), no. 1, 264-269

4.
V. N. Dixit, R. Kumar, and N. Ajmal, Fuzzy ideals and fuzzy prime ideals of a ring, Fuzzy Sets and Systems 44 (1991), no. 1, 127-138

5.
T. K. Dutta and B. K. Biswas, Fuzzy k-ideals of semirings, Bull. Calcutta Math. Soc. 87 (1995), no. 1, 91-96

6.
S. Ghosh, Fuzzy k-ideals of semirings, Fuzzy Sets and Systems 95 (1998), 103-108

7.
C. B. Kim, Isomorphism theorems and fuzzy k-ideals of k-semirings, Fuzzy Sets and Systems 112 (2000), 333-342

8.
R. Kumar, Fuzzy Algebra Volume I, University of Delhi Publication Division, 1993

9.
W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1982), no. 2, 133-139

10.
W. J. Liu, Operations on fuzzy ideals, Fuzzy Sets and Systems 11 (1983), no. 1, 31-41

11.
D. S. Malik and J. N. Mordeson, Fuzzy prime ideals of a ring, Fuzzy Sets and Systems 37 (1990), no. 1, 93-98

12.
T. K. Mukherjee and M. K. Sen, On fuzzy ideals of a ring I, Fuzzy Sets and Systems 21 (1987), no. 1, 99-104

13.
T. K. Mukherjee and M. K. Sen, Prime fuzzy ideals in rings, Fuzzy Sets and Systems 32 (1989), no. 3, 337-341

14.
A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517

15.
M. K. Sen and M. R. Adhikari, On k-ideals of semirings, Internat. J. Math. Math. Sci. 15 (1992), no. 2, 347-350

16.
U. M. Swamy and K. L. N. Swamy, Fuzzy prime ideals of rings, J. Math. Anal. Appl. 134 (1988), no. 1, 94-103

17.
X. Y. Xie, On prime, quasi-prime, weakly quasi-prime fuzzy left ideals of semi-groups, Fuzzy Sets and Systems 123 (2001), no. 2, 239-249

18.
Z. Yue, Prime L-fuzzy ideals and primary L-fuzzy ideals, Fuzzy Sets and Systems 27 (1988), no. 3, 345-350

19.
L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353