TY - JOUR T1 - 2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings AU - Onar, Serkan AU - Sönmez, Deniz AU - Yeşilot, Gürsel AU - Ersoy, Bayram Ali PY - 2019 DA - December Y2 - 2019 DO - 10.33187/jmsm.588093 JF - Journal of Mathematical Sciences and Modelling PB - Mahmut AKYİĞİT WT - DergiPark SN - 2636-8692 SP - 193 EP - 197 VL - 2 IS - 3 LA - en AB - 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. KW - 2-absorbing primary fuzzy ideals KW - 2-absorbing semiprimary fuzzy ideals CR - [1] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338-353. CR - [2] W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets Syst., 8 (1982), 133-139. CR - [3] T. K. Mukherjee, M.K. Sen, Prime fuzzy ideals in rings, Fuzzy Sets Syst. 32 (1989), 337-341. CR - [4] A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc., 75(3) (2007), 417-429. CR - [5] A. Badawi, U. Tekir, E. Yetkin, On 2-absorbing primary ideals in commutative rings, Bull. Austral. Math. Soc., 51(4) (2014), 1163-1173. CR - [6] T. K. Mukherjee, M. K. Sen, Primary fuzzy ideals and radical of fuzzy ideals, Fuzzy Sets Syst., 56 (1993), 97-101. CR - [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. CR - [8] V. N. Dixit, R. Kumar, N. Ajmal. Fuzzy ideals and fuzzy prime ideals of a ring, Fuzzy Sets Syst., 44 (1991), 127-138. CR - [9] L. I. Sidky, S. A. Khatab, Nil radical of fuzzy ideal, Fuzzy Sets Syst., 47 (1992), 117-120. CR - [10] S. Koc, R. N. Uregen, U. Tekir. On 2-absorbing quasi primary submodules, Filomat, 31 (2017), 2943-2950. CR - [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 . CR - [12] B. A. Ersoy, A generalization of cartesian product of fuzzy subgroups and ideals, J. Appl. Sci., 3 (2003), 100-102. UR - https://doi.org/10.33187/jmsm.588093 L1 - https://dergipark.org.tr/en/download/article-file/900164 ER -