Journals / Journal of Mathematical Sciences and Modelling / 2019 / Cilt: 2 Sayı: 3

2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings

Pages
193–197
Publication Date
2019-12-26
DOI
—
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AI Summary & Key Takeaways

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⚡ TL;DR(Too Long; Didn't Read)

Furthermore, we give some fundamental results concerning these notions.

📌 3 Key Takeaways

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Objective & Hypothesis:In this work, we introduce the notion of 2-absorbing semiprimary fuzzy ideal which is a generalization of semiprimary fuzzy ideal.
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Key Findings & Data: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 $.
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Conclusion & Impact:Furthermore, we give some fundamental results concerning these notions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:2-absorbing primary fuzzy ideals · 2-absorbing semiprimary fuzzy ideals

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.

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Cite This Article

SÖNMEZ, D., YEŞİLOT, G., ONAR, S., ERSOY, B. A. (2019). 2-Absorbing Semiprimary Fuzzy Ideal of Commutative Rings. Journal of Mathematical Sciences and Modelling, Cilt: 2 Sayı: 3, 193–197. https://ajindex.com/articles/908012

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References (12)

  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.