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. 
ON WEAKLY 2-ABSORBING PRIMARY IDEALS OF COMMUTATIVE RINGS
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
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
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
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
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
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
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
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
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
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
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 11 REFERENCES
On n-Absorbing Ideals of Commutative Rings
Let R be a commutative ring with 1 ≠ 0 and n a positive integer. In this article, we study two generalizations of a prime ideal. A proper ideal I of R is called an n-absorbing (resp., strongly
On 2-absorbing ideals of commutative rings
  • Ayman Badawi
  • Mathematics
    Bulletin of the Australian Mathematical Society
  • 2007
Suppose that R is a commutative ring with 1 ≠ 0. In this paper, we introduce the concept of 2-absorbing ideal which is a generalisation of prime ideal. A nonzero proper ideal I of R is called a
On 2-absorbing commutative semigroups and their applications to rings
A commutative ring R is called 2-absorbing (Badawi in Bull. Aust. Math. Soc. 75:417–429, 2007) if for arbitrary elements a,b,c∈R, abc=0 if and only if ab=0 or bc=0 or ac=0. In this paper we study
On Generalizations of Prime Ideals (II)
Let R be a commutative ring with identity. We say that a proper ideal P of R is (n − 1, n)-weakly prime (n ≥ 2) if 0 ≠ a 1…a n ∈ P implies a 1…a i−1 a i+1…a n ∈ P for some i ∈ {1,…, n}, where a 1,…,
Generalizations of Prime Ideals
Let R be a commutative ring with identity. Various generalizations of prime ideals have been studied. For example, a proper ideal I of R is weakly prime (resp., almost prime) if a, b ∈ R with ab ∈ I
ON THE 2-ABSORBING IDEALS
Multiplicative Ideal Theory, Queen Papers
  • Pure Appl. Math. 90,
  • 1992
Rings with Zero-Divisors, New York/Basil
  • 1988
...
1
2
...