Some results on 2-absorbing ideals in commutative semirings

Kumar, Prem; Dubey, Mithilesh Kumar; Sarohe, Poonam

doi:10.7862/rf.2015.7

Cited by 3 publications

(1 citation statement)

References 6 publications

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“…It has been studied extensively by many authors (e.g. [3], [7], [17] ). Darani [9] investigated and examined the notion of L-fuzzy 2-absorbing ideals and he has obtained interesting results on these concepts.…”

Section: Introductionmentioning

confidence: 99%

A study on fuzzy 2-absorbing primary Г-ideals in Г-rings

Onar

Sönmez

Ersoy

et al. 2017

Filomat

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In this paper, we initiate the study of a generalization of fuzzy primary Γ-ideals in Γ-rings by introducing fuzzy 2-absorbing primary Γ-ideals and fuzzy strongly 2-absorbing primary Γ-ideals. The notions of a fuzzy 2-absorbing primary Γ-ideal, fuzzy strongly 2-absorbing primary Γ-ideal and fuzzy weakly completely 2-absorbing primary Γ-ideal are defined and their structural characteristics and properties are investigated. The notion of a fuzzy K − 2-absorbing primary Γ-ideal is introduced and several of its properties are investigated. Finally, the relationships between fuzzy 2-absorbing primary Γ-ideals of a Γ-ring are examined.

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Section: Introductionmentioning

confidence: 99%

A study on fuzzy 2-absorbing primary Г-ideals in Г-rings

Onar

Sönmez

Ersoy

et al. 2017

Filomat

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On Weakly 1-Absorbing Primary Ideals of Commutative Semirings

Saleh

MURAA

2022

Communications in Advanced Mathematical Sciences

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Let R be a commutative semiring with $ 1 \neq0$ . In this paper, we study the concept of weakly 1-absorbing primary ideal which is a generalization of 1-absorbing ideal overccommutative semirings . A proper ideal I of R is called a weakly 1-absorbing primary ideal if whenever nonunit elements $a,b,c \in R$ and $0 \neq abc \in I$, then $ab \in I $or $c \in \sqrt{I}$. A number of results concerning weakly 1-absorbing primary ideals and examples of weakly 1-absorbing primary ideals are given. And we need a special type of ideals called k-ideal or subtractive ideal which is helps to prove results related to weakly 1-absorbing primary ideals. A subtractive ideal I of a semiring R is an ideal such that if $ x,x+y\in I$ ,then $ y\in I$

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On Fuzzy 2-absorbing Γ-ideals in Γ-rings

Onar

2022

Turkish Journal of Mathematics and Computer Science

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The goal of this paper is to give a definition of a generalization of fuzzy prime $\Gamma $-ideals in $\Gamma $-rings by introducing fuzzy 2-absorbing $\Gamma $-ideals and fuzzy weakly completely 2-absorbing $\Gamma $-ideals of commutative $\Gamma $-rings and to give their properties. Furthermore, we give a diagram which transition between definitions of fuzzy 2-absorbing $\Gamma $-ideals of a $\Gamma $-ring. Finally, we introduce fuzzy quotient $\Gamma $-ring of $R$ induced by the fuzzy weakly completely 2-absorbing $\Gamma $-ideal is a $2$-absorbing $\Gamma $-ring.

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Some results on 2-absorbing ideals in commutative semirings

Cited by 3 publications

References 6 publications

A study on fuzzy 2-absorbing primary Г-ideals in Г-rings

A study on fuzzy 2-absorbing primary Г-ideals in Г-rings

On Weakly 1-Absorbing Primary Ideals of Commutative Semirings

On Fuzzy 2-absorbing Γ-ideals in Γ-rings

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