English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

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

$\delta$-$r$-Hyperideals and $\phi$-$\delta$-$r$-Hyperideals of Commutative Krasner Hyperrings