Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
권호 표지
DOI QR코드

DOI QR Code

2-absorbing δ-semiprimary Ideals of Commutative Rings

  • Celikel, Ece Yetkin (Department of Electrical-Electronics Engineering, Faculty of Engineering, Hasan Kalyoncu University)
  • Received : 2020.12.18
  • Accepted : 2021.05.18
  • Published : 2021.12.31
Download PDF
⟨ Previous Next ⟩

Abstract

Let R be a commutative ring with nonzero identity, 𝓘(𝓡) the set of all ideals of R and δ : 𝓘(𝓡) → 𝓘(𝓡) an expansion of ideals of R. In this paper, we introduce the concept of 2-absorbing δ-semiprimary ideals in commutative rings which is an extension of 2-absorbing ideals. A proper ideal I of R is called 2-absorbing δ-semiprimary ideal if whenever a, b, c ∈ R and abc ∈ I, then either ab ∈ δ(I) or bc ∈ δ(I) or ac ∈ δ(I). Many properties and characterizations of 2-absorbing δ-semiprimary ideals are obtained. Furthermore, 2-absorbing δ1-semiprimary avoidance theorem is proved.

Keywords

References

  1. D. D. Anderson and M. Batanieh, Generalizations of prime ideals, Comm. Algebra, 36(2)(2008), 686-696. https://doi.org/10.1080/00927870701724177
  2. D. D. Anderson and M. Winders, Idealization of a module, J. Commut. Algebra, 1(1)(2009), 3-56. https://doi.org/10.1216/JCA-2009-1-1-3
  3. A. Badawi and B. Fahid, On weakly 2-absorbing δ-primary ideals of commutative rings, Georgian Math. J., 27(4)(2020), 503-516. https://doi.org/10.1515/gmj-2018-0070
  4. A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Austral. Math. Soc., 75(3)(2007), 417-429. https://doi.org/10.1017/S0004972700039344
  5. A. Badawi and A. Y. Darani, On weakly 2-absorbing ideals of commutative rings, Houston J. Math., 39(2)(2013), 441-452.
  6. A. Badawi, U. Tekir and E. Yetkin Celikel, On 2-absorbing primary ideals in commutative rings, Bull. Korean Math Soc., 51(4)(2014), 1163-117. https://doi.org/10.4134/BKMS.2014.51.4.1163
  7. A. Badawi, Unsal Tekir and E. Yetkin, On weakly 2-absorbing primary ideals in commutative rings, J. Korean Math. Soc., 52(1)(2015), 97-111. https://doi.org/10.4134/JKMS.2015.52.1.097
  8. A. Badawi, D. Sonmez and G. Yesilot, On weakly δ-semiprimary ideals of commutative rings, Algebra Colloquium, 25(3)(2018), 387-398. https://doi.org/10.1142/s1005386718000287
  9. J. Huckaba, Rings with zero-divisors, Marcel Dekker, New York/ Basil, 1988.
  10. I. Kaplansky, Commutative rings, rev. ed., University of Chicago, Chicago, 1974.
  11. C. P. Lu, Unions of Prime Submodules, Houston J. Math., 23(2)(1997), 203-213.
  12. Sh. Payrovi and S. Babaei, On 2-absorbing submodules, Algebra Colloq., 19(1)(2012), 913-920. https://doi.org/10.1142/S1005386712000776
  13. U. Tekir, S. Koc, K. H. Oral and K. P. Shum, On 2-Absorbing Quasi-Primary Ideals in Commutative Rings, Commun. Math. Stat., 4(1)(2016), 55-62. https://doi.org/10.1007/s40304-015-0075-9
  14. D. Zhao, δ-primary ideals of commutative rings, Kyungpook Math. J., 41(1)(2001), 17-22.