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Ideal-based quasi zero divisor graph
(Hacettepe Üniversitesi Fen Fakultesi, 2021)
Let R be a commutative ring with identity and I a proper ideal of R. In this paper we introduce the ideal-based quasi zero divisor graph QGammaI(R) of R with respect to I which is an undirected graph with vertex set ...
The triple zero graph of a commutative ring
(Ankara Üniv. Fen Fakültesi, 2021)
Let R be a commutative ring with non-zero identity. We define the set of triple zero elements of R by TZ(R)=ainZ(R)ast:$thereexists$b,cinRbackslash0$suchthat$abc=0$,$abneq0$,$acneq0$,$bcneq0. In this paper, we introduce ...
Semi n-ideals of commutative rings
(Springer Nature, 2022)
Let R be a commutative ring with identity. A proper ideal I is said to be an n-ideal of R if for a, b ∈ R, ab ∈ I and a∉0 imply b ∈ I. We give a new generalization of the concept of n-ideals by defining a proper ideal I ...
ON WEAKLY S-PRIME SUBMODULES
(Taehan Suhakhoe, 2022)
Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N:R M)∩S = ∅ to be weakly S-prime if there ...
δ-n-IDEALS OF COMMUTATIVE RINGS
(University of Guilan, 2022)
Let R be a commutative ring with non-zero identity, and δ: I(R) → I(R) be an ideal expansion where I(R) is the set of all ideals of R. In this paper, we introduce the concept of δ-n-ideals which is an extension of n-ideals ...
2-absorbing δ-semiprimary Ideals of Commutative Rings
(Kyungpook National University, 2021)
Let R be a commutative ring with nonzero identity, I(R) the set of all idealsof R and δ: I(R) → I(R) an expansion of ideals of R. In this paper, we introduce theconcept of 2-absorbing δ-semiprimary ideals in commutative ...
Generalizations of n-ideals of Commutative Rings
(Erzincan Binali Yıldırım Üniversitesi, Fen Bilimleri Enstitüsü, 2020)
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2-nil ideals of commutative rings
(Belgian Mathematical Society, 2021)
The concept of 2-nil ideal of a commutative ring R is introduced, as an alternative to the (2, n)-ideals from [6]. We study its relationship with previously introduced classes of ideals, such as 2-absorbing ideals and ...
On weakly 1 -absorbing primary submodules
(World Scientific, 2022)
In this paper, we introduce weakly 1-absorbing primary submodules of modules over commutative rings. Let R be a commutative ring with a nonzero identity and M be a nonzero unital module. A proper submodule N of M is said ...
2-Nil submodules of modules over commutative rings
(World Scientific, 2022)
In this paper, we extend the notion of 2-nil ideal introduced by Yetkin Celikel in [E. Yetkin Celikel, 2-nil ideals of commutative rings, Bulletin of the Belgian Mathematical Society Simon Stevin 28(3) (2021).] to 2-nil ...