DOI QR코드

DOI QR Code

ON 2-ABSORBING PRIMARY IDEALS IN COMMUTATIVE RINGS

Badawi, Ayman;Tekir, Unsal;Yetkin, Ece

  • 투고 : 2013.09.23
  • 발행 : 2014.07.31

초록

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

키워드

primary ideal;prime ideal;2-absorbing ideal;n-absorbing ideal

참고문헌

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  4. A. Y. Darani and E. R. Puczylowski, On 2-absorbing commutative semigroups and their applications to rings, Semigroup Forum 86 (2013), no. 1, 83-91. https://doi.org/10.1007/s00233-012-9417-z
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피인용 문헌

  1. On (m, n)-absorbing ideals of commutative rings vol.127, pp.2, 2017, https://doi.org/10.4134/BKMS.2014.51.4.1163
  2. On 2-Absorbing Quasi-Primary Ideals in Commutative Rings vol.4, pp.1, 2016, https://doi.org/10.4134/BKMS.2014.51.4.1163
  3. Weakly Classical Prime Submodules vol.56, pp.4, 2016, https://doi.org/10.4134/BKMS.2014.51.4.1163
  4. On 2-Absorbing Primary Submodules of Modules over Commutative Rings vol.24, pp.1, 2016, https://doi.org/10.4134/BKMS.2014.51.4.1163
  5. On 2-absorbing primary submodules of modules over commutative ring with unity vol.08, pp.04, 2015, https://doi.org/10.4134/BKMS.2014.51.4.1163
  6. On ϕ-2-Absorbing Primary Submodules vol.42, pp.1, 2017, https://doi.org/10.4134/BKMS.2014.51.4.1163
  7. ON n-ABSORBING IDEALS AND THE n-KRULL DIMENSION OF A COMMUTATIVE RING vol.53, pp.6, 2016, https://doi.org/10.4134/BKMS.2014.51.4.1163
  8. Onϕ-Absorbing Primary Elements in Lattice Modules vol.2015, 2015, https://doi.org/10.4134/BKMS.2014.51.4.1163
  9. ON 𝜙-n-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS vol.53, pp.3, 2016, https://doi.org/10.4134/BKMS.2014.51.4.1163
  10. On 2-Absorbing Primary Fuzzy Ideals of Commutative Rings vol.2017, 2017, https://doi.org/10.4134/BKMS.2014.51.4.1163
  11. On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative Semiring vol.56, pp.1, 2016, https://doi.org/10.4134/BKMS.2014.51.4.1163
  12. On (m,n)-closed ideals of commutative rings vol.16, pp.01, 2017, https://doi.org/10.4134/BKMS.2014.51.4.1163