# ON 2-ABSORBING PRIMARY IDEALS IN COMMUTATIVE RINGS

@article{Badawi2014ON2P, title={ON 2-ABSORBING PRIMARY IDEALS IN COMMUTATIVE RINGS}, author={Ayman Badawi and {\"U}nsal Tekir and Ece Yetkin}, journal={Bulletin of The Korean Mathematical Society}, year={2014}, volume={51}, pages={1163-1173} }

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

## 99 Citations

ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS

- Mathematics
- 2015

Let R be a commutative ring with 1 6 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…

On 2-Absorbing Quasi-Primary Ideals in Commutative Rings

- Mathematics
- 2016

Let R be a commutative ring with nonzero identity. In this article, we introduce the notion of 2-absorbing quasi-primary ideal which is a generalization of quasi-primary ideal. We define a proper…

Generalizations of 2-absorbing primaryideals of commutative rings

- Mathematics
- 2016

Let R be a commutative ring with 1 = 0 and S(R) be the set of all ideals of R . In this paper, we extend the concept of 2-absorbing primary ideals to the context of φ -2-absorbing primary ideals. Let…

On 2-absorbing primary ideals in commutative semirings

- Mathematics
- 2016

In this paper, we define 2-absorbing and weakly 2-absorbing primary ideals in a commutative semiring S with 1 ≠ 0 which are generalization of primary ideals of commutative ring. A proper ideal I of a…

n-Ideals of Commutative Rings

- Mathematics
- 2017

In this paper, we present a new classes of ideals: called n-ideal. Let R be a commutative ring with nonzero identity. We define a proper ideal I of R as an n-ideal if whenever ab ∈ I with a < √ 0,…

2-ABSORBING IDEALS IN FORMAL POWER SERIES RINGS

- Mathematics
- 2017

Let R be a commutative ring with identity. A proper ideal I of R is said to be 2−absorbing if whenever x1x2x3 ∈ I for x1, x2, x3 ∈ R, then there are 2 of the xi's whose product is in I. In this…

On strongly $1$-absorbing primary ideals of commutative rings

- Mathematics
- 2020

Let R be a commutative ring with 1 6= 0. In this paper, we introduce a subclass of the class of 1-absorbing primary ideals called the class of strongly 1-absorbing primary ideals. A proper ideal I of…

Uniformly 2-absorbing primary ideals of commutative rings

- Mathematics
- 2015

In this study, we introduce the concept of "uniformly 2-absorbing primary ideals" of commutative rings, which imposes a certain boundedness condition on the usual notion of 2-absorbing primary ideals…

On 1-absorbing primary ideals of commutative rings

- Mathematics, Art
- 2019

Let R be a commutative ring with nonzero identity. In this paper, we introduce the concept of 1-absorbing primary ideals in commutative rings. A proper ideal I of R is called a 1-absorbing primary ...

n-Absorbing Ideals of Commutative Rings and Recent Progress on Three Conjectures: A Survey

- Mathematics
- 2017

Let R be a commutative ring with 1 ≠ 0. Recall that a proper ideal I of R is called a 2-absorbing ideal of R if a, b, c ∈ R and abc ∈ I, then ab ∈ I or ac ∈ I or bc ∈ I. A more general concept than…

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