On Weakly Prime Fuzzy Ideals of Commutative Rings

Year 2019, Volume: 4 Issue: 1, 19 - 25, 15.04.2019

Deniz Sönmez Gürsel Yeşilot

https://doi.org/10.30931/jetas.404279

Abstract

In this paper, we present a new notion of fuzzy ideals : called
weakly prime fuzzy ideal. Let R be a commutative ring with non-zero identity.
A nonconstant fuzzy ideal µ of R is called weakly prime fuzzy ideal if 0_t !=
x_r y_s ∈ µ implies x_r ∈ µ or y_s ∈ µ for all t ∈ (0, µ(0)]. We investigate some
properties of this notion. Morever, it is established relations between weakly
prime ideals and weakly prime fuzzy ideals of commutative rings.

Keywords

weakly prime fuzzy ideals, prime fuzzy ideals

References

• [1] Anderson D. D. and Smith E., “Weakly prime ideals”, Houston J. Math. 29(4) (2003) : 831-840.
• [2] Atani S. E. and Farzalipour F., “On weakly primary ideals”, Georgian Math. J. 12(3) (2005) : 423-429.
• [3] Dixit V.N., Kumar R. and Ajmal N., “Fuzzy ideals and fuzzy prime ideals of a ring”, Fuzzy Sets and Systems 44 (1991) : 127-138.
• [4] Ersoy B.A., “A Generalization of Cartesian Product of Fuzzy Subgroups and Ideals”, Journal of Applied Sciences 3 (2003) : 100-102.
• [5] Liu W.J., “Fuzzy invariant subgroups and fuzzy ideals”, Fuzzy Sets and Systems 8 (1982) : 133-139.
• [6] Martinez L., “Fuzzy subgroups of fuzzy groups and fuzzy ideals of fuzzy rings”, J. Fuzzy Math. 3 (1995) : 833-849.
• [7] Mukherjee T.K. and Sen M.K., “Prime fuzzy ideals in rings”, Fuzzy Sets and Systems 32 (1989) : 337-341.
• [8] Zadeh L.A., “Fuzzy sets”, Inform and Control 8 (1965) : 338-353.