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2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings

Yıl 2019, Cilt: 2 Sayı: 3, 193 - 197, 26.12.2019
https://doi.org/10.33187/jmsm.588093

Öz

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.

Kaynakça

  • [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.
Yıl 2019, Cilt: 2 Sayı: 3, 193 - 197, 26.12.2019
https://doi.org/10.33187/jmsm.588093

Öz

Kaynakça

  • [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.
Toplam 12 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Deniz Sönmez 0000-0003-3186-4082

Gürsel Yeşilot 0000-0002-7279-9275

Serkan Onar 0000-0003-3084-7694

Bayram Ali Ersoy 0000-0002-8307-9644

Yayımlanma Tarihi 26 Aralık 2019
Gönderilme Tarihi 7 Temmuz 2019
Kabul Tarihi 27 Eylül 2019
Yayımlandığı Sayı Yıl 2019 Cilt: 2 Sayı: 3

Kaynak Göster

APA Sönmez, D., Yeşilot, G., Onar, S., Ersoy, B. A. (2019). 2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings. Journal of Mathematical Sciences and Modelling, 2(3), 193-197. https://doi.org/10.33187/jmsm.588093
AMA Sönmez D, Yeşilot G, Onar S, Ersoy BA. 2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings. Journal of Mathematical Sciences and Modelling. Aralık 2019;2(3):193-197. doi:10.33187/jmsm.588093
Chicago Sönmez, Deniz, Gürsel Yeşilot, Serkan Onar, ve Bayram Ali Ersoy. “2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings”. Journal of Mathematical Sciences and Modelling 2, sy. 3 (Aralık 2019): 193-97. https://doi.org/10.33187/jmsm.588093.
EndNote Sönmez D, Yeşilot G, Onar S, Ersoy BA (01 Aralık 2019) 2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings. Journal of Mathematical Sciences and Modelling 2 3 193–197.
IEEE D. Sönmez, G. Yeşilot, S. Onar, ve B. A. Ersoy, “2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings”, Journal of Mathematical Sciences and Modelling, c. 2, sy. 3, ss. 193–197, 2019, doi: 10.33187/jmsm.588093.
ISNAD Sönmez, Deniz vd. “2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings”. Journal of Mathematical Sciences and Modelling 2/3 (Aralık 2019), 193-197. https://doi.org/10.33187/jmsm.588093.
JAMA Sönmez D, Yeşilot G, Onar S, Ersoy BA. 2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings. Journal of Mathematical Sciences and Modelling. 2019;2:193–197.
MLA Sönmez, Deniz vd. “2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings”. Journal of Mathematical Sciences and Modelling, c. 2, sy. 3, 2019, ss. 193-7, doi:10.33187/jmsm.588093.
Vancouver Sönmez D, Yeşilot G, Onar S, Ersoy BA. 2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings. Journal of Mathematical Sciences and Modelling. 2019;2(3):193-7.

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