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ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

Unsal Tekir|Ayman Badawi|Ece Yetkin
대한수학회 (The Korean Mathematical Society)|2015.01|대한수학회지 (Journal of the KMS)|제52권 제1호|pp. 97-111

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참고문헌

키워드

n-absorbing idealprime ideal2-absorbing idealweakly prime idealprimary idealweakly primary idealweakly 2-absorbing ideal2-absorbing primary idealweakly 2-absorbing primary ideal
주제분류수학

초록

Let R be a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b, c ∈ R and 0 ≠ abc ∈ I, then ab ∈ I or ac ∈ √I or bc ∈ √I. A number of results concerning weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.

Abstract

Let R be a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of weakly 2-absorbing primary ideal which is a generalization of weakly 2-absorbing ideal. A proper ideal I of R is called a weakly 2-absorbing primary ideal of R if whenever a, b, c ∈ R and 0 ≠ abc ∈ I, then ab ∈ I or ac ∈ √I or bc ∈ √I. A number of results concerning weakly 2-absorbing primary ideals and examples of weakly 2-absorbing primary ideals are given.

참고문헌 (12)

  1. D. D. Anderson, "Generalizations of prime ideals", Comm. Algebra, 36(2), pp.686~696 (2008)
  2. D. D. Anderson, "Weakly prime ideals", Houston J. Math, 29(4), pp.831~840 (2003)
  3. D. F. Anderson, "On n-absorbing ideals of commutative rings", Comm. Algebra, 39(5), pp.1646~1672 (2011)
  4. S. Ebrahimi Atani, "On weakly primary ideals", Georgian Math. J, 12(3), pp.423~429 (2005)
  5. A. Badawi, "On 2-absorbing ideals of commutative rings", Bull. Austral. Math. Soc, 75(3), pp.417~429 (2007)
  6. A. Badawi, "On weakly 2-absorbing ideals of commutative rings", Hous-ton J. Math, 39(2), pp.441~452 (2013)
  7. A. Badawi, "On 2-absorbing primary ideals in commutative rings", Bull. Korean Math. Soc
  8. A. Y. Darani, "On 2-absorbing commutative semigroups and their applications to rings", Semigroup Forum, 86(1), pp.83~91 (2013)
  9. M. Ebrahimpour, "On generalizations of prime ideals", Comm. Algebra, 40(4), pp.1268~1279 (2012)
  10. R. Gilmer, "Multiplicative Ideal Theory", Queen’s Papers Pure Appl. Math, 90 (1992), Queen’s University
  11. J. Huckaba, "Rings with Zero-Divisors" (1988), Marcel Dekker
  12. S. Payrovi, "On the 2-absorbing ideals", Int. Math. Forum, 7(5-8), pp.265~271 (2012)

관련 논문AI추천

On 2-absorbing primary ideals in commutative ringsAyman Badawi, Ece Yetkin, Unsal Tekir대한수학회 · 대한수학회보2014 · 제51권 제4호On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative SemiringFatemeh Soheilnia경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2016 · 제56권 제1호ON WEAKLY 2-ABSORBING PRIMARY SUBMODULES OF MODULES OVER COMMUTATIVE RINGSAhmad Yousefian Darani, Fatemeh Soheilnia, Gulsen Ulucak, Unsal Tekir대한수학회 · 대한수학회지2017 · 제54권 제5호Some results on 1-absorbing primary and weakly 1-absorbing primary ideals of commutative ringsAli Yassine, Mohammad Javad Nikmehr, Reza Nikandish대한수학회 · 대한수학회보2021 · 제58권 제5호On 2-Absorbing and Weakly 2-Absorbing Ideals of Commutative SemiringsAhmad Yousefian Darani경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2012 · 제52권 제1호On $\phi$-$n$-absorbing primary ideals of commutative ringsAhmad Yousefian Darani, Hojjat Mostafanasab대한수학회 · 대한수학회지2016 · 제53권 제3호

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