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Journals / Hacettepe Journal of Mathematics and Statistics / 2026 / Volume: 48 Issue: 3

On graded 2-absorbing and graded weakly 2-absorbing ideals

Khaldoun Al-zoubi0000-0001-6082-4480
Rashid Abu-dawwas0000-0001-8998-7590
Seçil Çeken0000-0002-7578-9320
Pages
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Publication Date
2019-06-15
DOI
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

We investigate graded (weakly) 2-absorbing ideals of $R_{1}\times R_{2}$ where $R_{1}$ and $R_{2}$ are two graded rings.

📌 3 Key Takeaways

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Objective & Hypothesis:In this paper, we introduce and study graded 2-absorbing and graded weakly 2-absorbing ideals of a graded ring which are different from 2-absorbing and weakly 2-absorbing ideals.
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Key Findings & Data:We give some properties and characterizations of these ideals and their homogeneous components.
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Conclusion & Impact:We investigate graded (weakly) 2-absorbing ideals of $R_{1}\times R_{2}$ where $R_{1}$ and $R_{2}$ are two graded rings.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:graded 2-absorbing ideal · graded weakly 2-absorbing ideal · graded weakly prime ideal

Abstract

In this paper, we introduce and study graded 2-absorbing and graded weakly 2-absorbing ideals of a graded ring which are different from 2-absorbing and weakly 2-absorbing ideals. We give some properties and characterizations of these ideals and their homogeneous components. We investigate graded (weakly) 2-absorbing ideals of $R_{1}\times R_{2}$ where $R_{1}$ and $R_{2}$ are two graded rings.

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Cite This Article

Al-zoubi, K., Abu-dawwas, R., Çeken, S. (2019). On graded 2-absorbing and graded weakly 2-absorbing ideals. Hacettepe Journal of Mathematics and Statistics, Volume: 48 Issue: 3. https://ajindex.com/articles/1402787

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References (14)

  1. D.F. Anderson and A. Badawi, On n-absorbing ideals of commutative rings, Comm. Algebra 39 (5), 1646-1672, 2011.
  2. D.D. Anderson and E. Smith, Weakly prime ideals, Houston J. Math. 29 (4), 831-840, 2003.
  3. S.E. Atani, On graded weakly prime ideals. Turk. J. Math. 30 (4), 351-358, 2006.
  4. A. Badawi, On 2-absorbing ideals of commutative rings, Bull. Aust. Math. Soc. 75 (3), 417-429, 2007.
  5. A. Badawi and A.Y. Darani,On weakly 2-absorbing ideals of commutative rings, Hous- ton J. Math. 39 (2), 441-452, 2013.
  6. N.H. McCoy, A note on finite unions of ideals and subgroups, Proc. Amer. Math. Soc. 8, 633-637, 1957.
  7. C. Nastasescu and V.F. Oystaeyen, Graded Ring Theory, Mathematical Library 38, North Holand, Amsterdam, 1983.
  8. C. Nastasescu and V.F. Oystaeyen, Methods of Graded Rings, LNM 1836, Springer- Verlag, Berlin-Heidelberg, 2004.
  9. S.H. Payrovi and S. Babaei, On 2-absorbing submodules, Algebra Collq. 19, 913-920, 2012.
  10. S.H. Payrovi and S. Babaei, On the 2-absorbing ideals, Int. Math. Forum 7 (6), 265- 271, 2012.
  11. S.H. Payrovi and S. Babaei, On the 2-absorbing ideals in commutative rings, Bull. Malays. Math. Soc. 23, 1511-1526, 2013.
  12. P.Jr. Quartaro and H.S. Butts, Finite unions of ideals and modules, Proc. Amer. Math. Soc. 52, 91-96, 1975.
  13. M. Refai and K. Al-Zoubi, On graded primary ideals, Turk. J. Math. 28 (3), 217-229, 2004.
  14. A. Yousefian-Darani and F. Soheilnia, 2-absorbing and weakly 2-absorbing submodules, Thai J. Math. 9 (3), 577-584, 2011.