2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings

Year 2019, Volume: 2 Issue: 3, 193 - 197, 26.12.2019

Deniz Sönmez , Gürsel Yeşilot , Serkan Onar , Bayram Ali Ersoy

https://doi.org/10.33187/jmsm.588093

https://izlik.org/JA98JH29UE

Abstract

In this work, we introduce the notion of 2-absorbing semiprimary fuzzy  ideal which is a generalization of semiprimary fuzzy ideal. Let $ R $ be a ring. Then the nonconstant fuzzy ideal $ \mu $ is called a 2-absorbing semiprimary fuzzy ideal if  $ \sqrt{\mu } $ is a 2-absorbing fuzzy ideal of $ R $. Furthermore, we give some fundamental results concerning these notions.

Keywords

2-absorbing primary fuzzy ideals , 2-absorbing semiprimary fuzzy ideals

References

• [1] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353.
• [2] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets Syst., 8 (1982), 133-139.
• [3] T. K. Mukherjee, M.K. Sen, Prime fuzzy ideals in rings, Fuzzy Sets Syst. 32 (1989), 337-341.
• [4] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc., 75(3) (2007), 417-429.
• [5] A. Badawi, U. Tekir, E. Yetkin, On 2-absorbing primary ideals in commutative rings, Bull. Austral. Math. Soc., 51(4) (2014), 1163-1173.
• [6] T. K. Mukherjee, M. K. Sen, Primary fuzzy ideals and radical of fuzzy ideals, Fuzzy Sets Syst., 56 (1993), 97-101.
• [7] D. S¨onmez, G. Yes¸ilot, S. Onar, B. A. Ersoy, B. Davvaz, On 2-absorbing primary fuzzy ideals of commutative rings, Math. Probl. Eng., (2017), doi:10.1155/2017/5485839.
• [8] V. N. Dixit, R. Kumar, N. Ajmal. Fuzzy ideals and fuzzy prime ideals of a ring, Fuzzy Sets Syst., 44 (1991), 127-138.
• [9] L. I. Sidky, S. A. Khatab, Nil radical of fuzzy ideal, Fuzzy Sets Syst., 47 (1992), 117-120.
• [10] S. Koc, R. N. Uregen, U. Tekir. On 2-absorbing quasi primary submodules, Filomat, 31 (2017), 2943-2950.
• [11] F. Callialp, E. Yetkin, U. Tekir, On 2-absorbing primary and weakly 2-absorbing primary elements in multiplicative lattices, Ital. J. Pure Appl. Math., 34 (2015), 263-276 .
• [12] B. A. Ersoy, A generalization of cartesian product of fuzzy subgroups and ideals, J. Appl. Sci., 3 (2003), 100-102.