TY - JOUR T1 - On Weakly Prime Fuzzy Ideals of Commutative Rings AU - Sönmez, Deniz AU - Yeşilot, Gürsel PY - 2019 DA - April DO - 10.30931/jetas.404279 JF - Journal of Engineering Technology and Applied Sciences JO - JETAS PB - Muhammet KURULAY WT - DergiPark SN - 2548-0391 SP - 19 EP - 25 VL - 4 IS - 1 LA - en AB - In this paper, we present a new notion of fuzzy ideals : calledweakly 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 someproperties of this notion. Morever, it is established relations between weaklyprime ideals and weakly prime fuzzy ideals of commutative rings. KW - weakly prime fuzzy ideals KW - prime fuzzy ideals CR - [1] Anderson D. D. and Smith E., “Weakly prime ideals”, Houston J. Math. 29(4) (2003) : 831-840. CR - [2] Atani S. E. and Farzalipour F., “On weakly primary ideals”, Georgian Math. J. 12(3) (2005) : 423-429. CR - [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. CR - [4] Ersoy B.A., “A Generalization of Cartesian Product of Fuzzy Subgroups and Ideals”, Journal of Applied Sciences 3 (2003) : 100-102. CR - [5] Liu W.J., “Fuzzy invariant subgroups and fuzzy ideals”, Fuzzy Sets and Systems 8 (1982) : 133-139. CR - [6] Martinez L., “Fuzzy subgroups of fuzzy groups and fuzzy ideals of fuzzy rings”, J. Fuzzy Math. 3 (1995) : 833-849. CR - [7] Mukherjee T.K. and Sen M.K., “Prime fuzzy ideals in rings”, Fuzzy Sets and Systems 32 (1989) : 337-341. CR - [8] Zadeh L.A., “Fuzzy sets”, Inform and Control 8 (1965) : 338-353. UR - https://doi.org/10.30931/jetas.404279 L1 - https://dergipark.org.tr/en/download/article-file/706099 ER -