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Intuitionistic Fuzzy 2-Absorbing Primary Ideals of Commutative Rings

Yıl 2018, Cilt: 8, 37 - 48, 30.06.2018

Öz

The aim of this paper is to give a definition of intuitionistic fuzzy 2-absorbing primary ideal and intuitionistic fuzzy weakly completely 2-absorbing primary ideals of commutative rings and to give their properties. Moreover, we give a diagram of transition between definitions of intuitionistic fuzzy 2- absorbing primary ideals of commutative rings.

Kaynakça

  • Anderson, D. F., Badawi, A., On n- absorbing ideals of commutative rings, Comm. Algebra, 39(2011), 1646-1672.
  • Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87-96.
  • Badawi, A., On 2- absorbing ideals of commutative rings, Bull. Austral. Math. Soc., 75(2007), 417-429.
  • Badawi, A., Darani, A. Y., On weakly 2-absorbing ideals of commutative rings, Houston Math., 39(2013), 441-452.
  • Badawi, A., Tekir, U., Yetkin, E., On 2- absorbing primary ideals in commutative rings, Bull. Austral. Math. Soc., 51(2014), 1163-1173.
  • Bakhadach, I., Melliani, S., Oukessou, M., Chadli, L. S., Intuitionistic fuzzy ideal and intuitionistic fuzzy prime ideal in a ring, Intuitionistic Fuzzy Sets (ICIFSTA), 22(2)(2016), 59-63.
  • Darani, A. Y., On L- fuzzy 2- absorbing ideals, Italian J. of Pure and Appl. Math., 36(2016), 147-154.
  • Darani, A. Y., Hashempoor, A., L-fuzzy 0-(1-or 2-or 3-) 2-absorbing ideals in semiring, Annals of Fuzzy Math. and Inform., 7(2014), 303-311.
  • Darani, A. Y., Puczylowski, E. R., On 2-absorbing commutative semigroups and their applications to rings, Semigroup Forum, 86(2013), 83-91.
  • Hur, K., Kang, H. W., Song, H. K., Intuitionistic fuzzy subgroups and subrings, Honam Math J., 25(2003), 19-41.
  • Kumar, P., Dubey, M. K., Sarohe, P., Some results on 2-absorbing ideals in commutative semirings, J.Math and Application, 38(2015), 77-84.
  • Liu, W. J., Operation on fuzzy ideals, Fuzzy Sets and Systems, 11(1983), 31-4.
  • Marasdeh, M. F., Salleh A. R., Intuitionistic fuzzy rings, International Journal of Algebra, 5(2011), 37-47.
  • Mukherjee, T. K., Sen, M. K., Operation on fuzzy ideals, Fuzzy Sets and Systems, 32(1989), 337-341.
  • Mukherjee, T. K., Sen, M. K., Primary fuzzy ideals and radical of fuzzy ideals, Fuzzy Sets and Systems, 56(1993), 97-101.
  • Palanivelrajan, M., Nandakumar, S., Some properties of intuitionistic fuzzy primary and semiprimary ideals, Notes on Intuitionistic Fuzzy Sets, 18(2012), 68-74.
  • Rossenfeld, A., Fuzzy groups, J. Math. Anal. Appl., 35(1971), 512-517.
  • Sharma, P. K., Translates of intuitionistic fuzzy subring, International Review of Fuzzy Mathematics, 6(2)(2011), 77-84.
  • Sidky, L. I., Khatab, S. A., Nil radical of fuzzy ideal, Fuzzy Sets and Systems, 47(1992), 117-120.
  • Sonmez, D., Yesilot, G., Onar, S., Ersoy, B. A., Davvaz, B., On 2-absorbing primary fuzzy ideals of commutative rings, Mathematical Problems In Engineering, ID:5485839(2017).
  • Yavuz, S., Onar, S., Ersoy, B. A., Sonmez, D., Intuitionistic fuzzy 2-absorbing ideals of commutative rings, Journal of Hyperstructures, 2017.
  • Zadeh, L., Fuzzy sets, Inform. and Control, 8(1965), 338-353. 1
Yıl 2018, Cilt: 8, 37 - 48, 30.06.2018

Öz

Kaynakça

  • Anderson, D. F., Badawi, A., On n- absorbing ideals of commutative rings, Comm. Algebra, 39(2011), 1646-1672.
  • Atanassov, K., Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87-96.
  • Badawi, A., On 2- absorbing ideals of commutative rings, Bull. Austral. Math. Soc., 75(2007), 417-429.
  • Badawi, A., Darani, A. Y., On weakly 2-absorbing ideals of commutative rings, Houston Math., 39(2013), 441-452.
  • Badawi, A., Tekir, U., Yetkin, E., On 2- absorbing primary ideals in commutative rings, Bull. Austral. Math. Soc., 51(2014), 1163-1173.
  • Bakhadach, I., Melliani, S., Oukessou, M., Chadli, L. S., Intuitionistic fuzzy ideal and intuitionistic fuzzy prime ideal in a ring, Intuitionistic Fuzzy Sets (ICIFSTA), 22(2)(2016), 59-63.
  • Darani, A. Y., On L- fuzzy 2- absorbing ideals, Italian J. of Pure and Appl. Math., 36(2016), 147-154.
  • Darani, A. Y., Hashempoor, A., L-fuzzy 0-(1-or 2-or 3-) 2-absorbing ideals in semiring, Annals of Fuzzy Math. and Inform., 7(2014), 303-311.
  • Darani, A. Y., Puczylowski, E. R., On 2-absorbing commutative semigroups and their applications to rings, Semigroup Forum, 86(2013), 83-91.
  • Hur, K., Kang, H. W., Song, H. K., Intuitionistic fuzzy subgroups and subrings, Honam Math J., 25(2003), 19-41.
  • Kumar, P., Dubey, M. K., Sarohe, P., Some results on 2-absorbing ideals in commutative semirings, J.Math and Application, 38(2015), 77-84.
  • Liu, W. J., Operation on fuzzy ideals, Fuzzy Sets and Systems, 11(1983), 31-4.
  • Marasdeh, M. F., Salleh A. R., Intuitionistic fuzzy rings, International Journal of Algebra, 5(2011), 37-47.
  • Mukherjee, T. K., Sen, M. K., Operation on fuzzy ideals, Fuzzy Sets and Systems, 32(1989), 337-341.
  • Mukherjee, T. K., Sen, M. K., Primary fuzzy ideals and radical of fuzzy ideals, Fuzzy Sets and Systems, 56(1993), 97-101.
  • Palanivelrajan, M., Nandakumar, S., Some properties of intuitionistic fuzzy primary and semiprimary ideals, Notes on Intuitionistic Fuzzy Sets, 18(2012), 68-74.
  • Rossenfeld, A., Fuzzy groups, J. Math. Anal. Appl., 35(1971), 512-517.
  • Sharma, P. K., Translates of intuitionistic fuzzy subring, International Review of Fuzzy Mathematics, 6(2)(2011), 77-84.
  • Sidky, L. I., Khatab, S. A., Nil radical of fuzzy ideal, Fuzzy Sets and Systems, 47(1992), 117-120.
  • Sonmez, D., Yesilot, G., Onar, S., Ersoy, B. A., Davvaz, B., On 2-absorbing primary fuzzy ideals of commutative rings, Mathematical Problems In Engineering, ID:5485839(2017).
  • Yavuz, S., Onar, S., Ersoy, B. A., Sonmez, D., Intuitionistic fuzzy 2-absorbing ideals of commutative rings, Journal of Hyperstructures, 2017.
  • Zadeh, L., Fuzzy sets, Inform. and Control, 8(1965), 338-353. 1
Toplam 22 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Makaleler
Yazarlar

Sanem Yavuz Bu kişi benim

Serkan Onar 0000-0003-3084-7694

Deniz Sönmez Bu kişi benim

Bayram Ali Ersoy

Gürsel Yeşilot

Yayımlanma Tarihi 30 Haziran 2018
Yayımlandığı Sayı Yıl 2018 Cilt: 8

Kaynak Göster

APA Yavuz, S., Onar, S., Sönmez, D., Ersoy, B. A., vd. (2018). Intuitionistic Fuzzy 2-Absorbing Primary Ideals of Commutative Rings. Turkish Journal of Mathematics and Computer Science, 8, 37-48.
AMA Yavuz S, Onar S, Sönmez D, Ersoy BA, Yeşilot G. Intuitionistic Fuzzy 2-Absorbing Primary Ideals of Commutative Rings. TJMCS. Haziran 2018;8:37-48.
Chicago Yavuz, Sanem, Serkan Onar, Deniz Sönmez, Bayram Ali Ersoy, ve Gürsel Yeşilot. “Intuitionistic Fuzzy 2-Absorbing Primary Ideals of Commutative Rings”. Turkish Journal of Mathematics and Computer Science 8, Haziran (Haziran 2018): 37-48.
EndNote Yavuz S, Onar S, Sönmez D, Ersoy BA, Yeşilot G (01 Haziran 2018) Intuitionistic Fuzzy 2-Absorbing Primary Ideals of Commutative Rings. Turkish Journal of Mathematics and Computer Science 8 37–48.
IEEE S. Yavuz, S. Onar, D. Sönmez, B. A. Ersoy, ve G. Yeşilot, “Intuitionistic Fuzzy 2-Absorbing Primary Ideals of Commutative Rings”, TJMCS, c. 8, ss. 37–48, 2018.
ISNAD Yavuz, Sanem vd. “Intuitionistic Fuzzy 2-Absorbing Primary Ideals of Commutative Rings”. Turkish Journal of Mathematics and Computer Science 8 (Haziran 2018), 37-48.
JAMA Yavuz S, Onar S, Sönmez D, Ersoy BA, Yeşilot G. Intuitionistic Fuzzy 2-Absorbing Primary Ideals of Commutative Rings. TJMCS. 2018;8:37–48.
MLA Yavuz, Sanem vd. “Intuitionistic Fuzzy 2-Absorbing Primary Ideals of Commutative Rings”. Turkish Journal of Mathematics and Computer Science, c. 8, 2018, ss. 37-48.
Vancouver Yavuz S, Onar S, Sönmez D, Ersoy BA, Yeşilot G. Intuitionistic Fuzzy 2-Absorbing Primary Ideals of Commutative Rings. TJMCS. 2018;8:37-48.