On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative Semiring

Soheilnia, Fatemeh

doi:10.5666/kmj.2016.56.1.107

Cited by 9 publications

(6 citation statements)

References 9 publications

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“…Many authors studied on this issue, (see for example [4,7,9,13,15,17]). The notion of δ−primary ideals in commutative rings was introduced by Zhao in [18]. This concept is considered to unify prime and primary ideals.…”

Section: Introductionmentioning

confidence: 99%

On weakly (m, n)−closed δ−primary ideals of commutative rings

Hamoda,

Issoual

2023

Proyecciones (Antofagasta)

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Let R be a commutative ring with 1 ≠ 0. In this article, we introduce the concept of weakly (m, n)−closed δ−primary ideals of R and explore its basic properties. We show that a proper ideal I of R is a weakly (m, n)−closed γ ◦ δ−primary ideal of R if and only if I is an (m, n)−closed γ ◦ δ−primary ideal of R, where δ and γ are expansions ideals of R with δ(0) is an (m, n)−closed γ−primary ideal of R. Furthermore, we provide examples to demonstrate the validity and applicability of our results.

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Section: Introductionmentioning

confidence: 99%

On weakly (m, n)−closed δ−primary ideals of commutative rings

Hamoda,

Issoual

2023

Proyecciones (Antofagasta)

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“…The question was whether a unified approach to studying these two structures is possible. In [14], Dongsheng presented the concept of δ-primary ideals unifing the prime and primary ideals under one frame in a commutative ring. Furthermore, Fahid and Dongsheng put two concepts of 2-absorbing ideals and 2-absorbing primary ideals in one frame called 2-absorbing δ-primary ideals in [15].…”

Section: Introductionmentioning

confidence: 99%

Unifing the prime and primary hyperideals under one frame in a Krasner (m, n)-hyperring

Anbarloei

2021

Communications in Algebra

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The notions of N -hyperideals and J-hyperideals as two new classes of hyperideals were recently defined in the context of Krasner (m, n)-hyperrings. These concepts are created on the basis of the intersection of all n-ary prime hyperideals and the intersection of all maximal hyperideals, respectively. Despite being vastly different in many aspects, they share numerous similar properties. The aim of this research work is to merge them under one frame called n-ary δ(0)-hyperideals where the function δ assigns to each hyperideal of a Krasner (m, n)-hyperring a hyperideal of the same hyperring. We give various properties of n-ary δ(0)-hyperideals and use them to characterize certain classes of hyperrings such as hyperintegral domains and local hyperrings. Moreover, we introduce the notions of (s, n)-absorbing δ(0)-hypereideals and weakly (s, n)absorbing δ(0)-hypereideals.

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“…Note that every graded prime ideal is also a graded 2-absorbing ideal. After this, graded 2-absorbing version of graded ideals and many generalizations of graded 2-absorbing ideals attracted considerable attention by many researchers in [2,16,18]. In [9], the authors defined the notion of graded almost prime ideals.…”

Section: Introductionmentioning

confidence: 99%

On Graded $ϕ$-$1$-absorbing prime ideals

Refai,

Abu-Dawwas,

Tekir

et al. 2021

Preprint

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Let G be a group, R be a G-graded commutative ring with nonzero unity and GI(R) be the set of all graded ideals of R. Suppose that φ : GI(R) → GI(R) ∪ {∅} is a function. In this article, we introduce and study the concept of graded φ-1-absorbing prime ideals. A proper graded ideal I of R is called a graded φ-1-absorbing prime ideal of R if whenever a, b, c are homogeneous nonunit elements of R such that abc ∈ I − φ(I), then ab ∈ I or c ∈ I. Several properties of graded φ-1-absorbing prime ideals have been examined.

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On 2-Absorbing and Weakly 2-Absorbing Primary Ideals of a Commutative Semiring

Cited by 9 publications

References 9 publications

On weakly (m, n)−closed δ−primary ideals of commutative rings

On weakly (m, n)−closed δ−primary ideals of commutative rings

Unifing the prime and primary hyperideals under one frame in a Krasner (m, n)-hyperring

On Graded $ϕ$-$1$-absorbing prime ideals

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