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arXiv · 2112.05513

$δ$-$r$-Hyperideals and $ϕ$-$δ$-$r$-Hyperideals of Commutative Krasner Hyperrings

Peng Xu·Melis Bolat·Elif Kaya·Serkan Onar·Bayram Ali Ersoy·Kostaq Hila
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Abstract

In this paper, our purpose is to define the expansion of $r$-hyperideals and extend this concept to $ϕ$-$δ$-$r$-hyperideal. Let $\Re$ be a commutative Krasner hyperring with nonzero identity. Given an expansion $δ$ of hyperideals, a proper hyperideal $N$ of $\Re$ is called $δ$-$r$-hyperideal if $a\cdot b\in N$ with $ann(a)=0$ implies that $b\in δ(N)$, for all $a,b\in\Re$. Therefore, given an expansion $δ$ of hyperideals and a hyperideal reduction $ϕ$, a proper hyperideal $N$ of $\Re$ is called $ϕ$-$δ$-$r$-hyperideal if $a\cdot b\in N-ϕ(N)$ with $ann(a)=0$ implies that $b\inδ(N)$, for all $a,b\in\Re$. We investigate some of their properties and give some examples.

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Peng Xu, Melis Bolat, Elif Kaya, Serkan Onar, Bayram Ali Ersoy, Kostaq Hila. 2022-04-05. $δ$-$r$-Hyperideals and $ϕ$-$δ$-$r$-Hyperideals of Commutative Krasner Hyperrings. https://arxiv.org/abs/2112.05513

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