arXiv subjects

Elif Kaya

Publications and source records attributed to Elif Kaya.

3 recordsLinked to original sources

arXiv2022

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

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.

math.GM↗

arXiv2022

$r$-Hyperideals and Generalizations of $r$-Hyperideals in Krasner Hyperrings

In this study, we examine some properties of $r$-hyperideals in the commutative Krasner hyperrings. Some properties of $pr$-hyperideals are also studied. The relation between prime hyperideals and $r$-hyperideals is investigated. We show that the image and the inverse image of an $r$-hyperideal is also an $r$-hyperideal. We also introduce a generalization of r-hyperideals and we prove some properties of them.

math.GM↗

arXiv2021

$ϕ$-$δ$-Primary Hyperideals in Krasner Hyperrings

In this paper, we study commutative Krasner hyperring with nonzero identity. $ϕ$-prime, $ϕ$-primary and $ϕ$-$δ$-primary hyperideals are introduced. We intend to extend the concept of $δ$-primary hyperideals to $ϕ$-$δ$-primary hyperideals. We give some characterizations of hyperideals to classify them. We denote the set of all hyperideals of $\Re$ by $L(\Re)$ (all proper hyperideals of $\Re$ by $L^{\ast }(\Re)).$ Let $ϕ$ be a reduction function such that $ϕ:L(\Re)\rightarrow L(\Re)\cup\{\emptyset\}$ and $δ$ be an expansion function such that $δ:L(\Re)\rightarrow L(\Re).$ $N$ be a proper hyperideal of $\Re.$ $N$ is called $ϕ$-$δ$-primary hyperideal of $\Re$ if $a\circ b\in N-$ $ϕ(N),$ then $a\in N$ or $b\inδ(N),$ for some $a,b\in\Re.$ We\ discuss the relation between $ϕ$-$δ$-primary hyperideal and other hyperideals.

math.GM↗