Generalizations of 2-absorbing primaryideals of commutative rings

Abstract

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 ϕ : S(R) → S(R) ∪ ∅ be a function. A proper ideal I of R is said to be a ϕ -2-absorbing primary ideal of R if whenever a, b, c ∈ R with abc ∈ I − ϕ(I) implies ab ∈ I or ac ∈ √ I or bc ∈ √ I . A number of results concerning ϕ -2-absorbing primary ideals are given.

Değişmeli Halkalarda n-ideallerin Genelleştirmeleri

“…Recall from Khaksari (2015) that is called a − 2-absorbing ideal of if whenever , , ∈ and ∈ − ( ), then either ∈ or ∈ or ∈ . The concept of −2-absorbing primary ideals is first introduced and studied in Badawi et al (2016): is called a − 2-absorbing primary ideal of if whenever , , ∈ and ∈ − ( ), then either ∈ or ∈ √ or ∈ √ . In a recent study U.…”

Generalization of 2-absorbing quasi primary ideals

“…However, it is clear that I is a 2-absorbing primary ideal of Z, since 2.5 ∈ √ I. In 2016, the authors introduced the concept of φ-2-absorbing primary ideal which a proper ideal I of R is called a φ-2-absorbing primary ideal of R if whenever a, b, c ∈ R and abc ∈ I − φ(I), then ab ∈ I or ac ∈ √ I or bc ∈ √ I, see [9].…”

On phi-2-Absorbing phi‎-2-Absorbing Primary Hyperideals of A Multiplicative Hyperring

“…The notion of φ-ideal was studied by Anderson in [2]. The purpose of the paper is to generalize the idea of φ-prime ideal as in [2], [3] and [4] to the context of hyperideals of hyperrings.…”