A study on a generalization of the n-ary prime hyperideals in a Krasner (m, n)-hyperring

Anbarloei, Mahdi

doi:10.1007/s13370-021-00878-6

Cited by 2 publications

(1 citation statement)

References 10 publications

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“…Let I ⊆ ∪ n i=1 I i for some n-ary S-prime hyperideals I n 1 of R. For each 1 ≤ i ≤ n, we get s i ∈ S such that (I i : s i ) is an n-ary prime hyperideal of R, by Theorem 3.4. Since I ⊆ ∪ n i=1 I i ⊆ ∪ n i=1 (I i : s i ), we have I ⊆ (I i : s i ) for some 1 ≤ i ≤ n, by Theorem 5.1 in [4]. Thus g(s i , I, 1 (n−2) ) ⊆ I i .…”

Section: N-ary S-prime Hyperidealsmentioning

confidence: 88%

Extensions of $n$-ary prime hyperideals via an $n$-ary multiplicative subset in a Krasner $(m,n)$-hyperring

Anbarloei¹

2022

Preprint

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Let R be a Krasner (m, n)-hyperring and S be an n-ary multiplicative subset of R. The purpose of this paper is to introduce the notion of n-ary S-prime hyperideals as a new expansion of n-ary prime hyperideals. A hyperideal I of R disjoint with S is said to be an n-ary S-prime hyperideal if there exists s ∈ S such that whenever g(x n 1 ) ∈ I for all x n 1 ∈ R, then g(s, x i , 1 (n−2) ) ∈ I for some 1 ≤ i ≤ n. Several properties and characterizations concerning n-ary S-prime hyperideals are presented. The stability of this new concept with respect to various hyperring-theoretic constructions are studied. Furthermore, we extend this concept to n-ary S-primary hyperideals. We obtained some specific results explaining the structure.2010 Mathematics Subject Classification. 16Y99. Key words and phrases.n-ary J-hyperideal, n-ary δ-J-hyperideal, (k, n)-absorbing δ-Jhyperideal.

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Section: N-ary S-prime Hyperidealsmentioning

confidence: 88%

Extensions of $n$-ary prime hyperideals via an $n$-ary multiplicative subset in a Krasner $(m,n)$-hyperring

Anbarloei¹

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Extensions of n-ary prime hyperideals via an n-ary multiplicative subset in a Krasner (m,n)-hyperring

Anbarloei

2023

Filomat

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Let R be a Krasner (m, n)-hyperring and S be an n-ary multiplicative subset of R. The purpose of this paper is to introduce the notion of n-ary S-prime hyperideals as a new expansion of n-ary prime hyperideals. A hyperideal I of R disjoint with S is said to be an n-ary S-prime hyperideal if there exists s ? S such that whenever 1(xn1) ? I for all xn1 ? R, then 1(s,xi,1(n?2)) ? I for some 1 ? i ? n. Several properties and characterizations concerning n-ary S-prime hyperideals are presented. The stability of this new concept with respect to various hyperring-theoretic constructions are studied. Furthermore, the concept of n-ary S-primary hyperideals is introduced. Several properties of them are provided.

show abstract

A study on a generalization of the n-ary prime hyperideals in a Krasner (m, n)-hyperring

Cited by 2 publications

References 10 publications

Extensions of $n$-ary prime hyperideals via an $n$-ary multiplicative subset in a Krasner $(m,n)$-hyperring

Extensions of $n$-ary prime hyperideals via an $n$-ary multiplicative subset in a Krasner $(m,n)$-hyperring

Extensions of n-ary prime hyperideals via an n-ary multiplicative subset in a Krasner (m,n)-hyperring

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