فهرست نشریات علمی دسترسی آزاد ایران

Various expansions of prime hyperideals have been studied in a Krasner $(m,n)$-hyperring $R$. For instance, a proper hyperideal $Q$ of $R$ is called weakly $(k,n)$-absorbing (primary) provided that for $r_1^{kn-k+1} \in R$, $g(r_1^{kn-k+1}) \in Q-\{0\}$ implies that there are $(k-1)n-k+2$ of the $r_i^,$s whose $g$-product is in $Q$ $\Bigl ($ $g(r_1^{(k-1)n-k+2}) \in Q$ or a $g$-product of $(k-1)n-k+2$ of $r_i^,$s ,except $g(r_1^{(k-1)n-k+2})$, is in $\boldsymbol{ r}^{(m,n)}(Q)$ $\Bigr )$. In this paper, we aim to extend the notions to the concepts of $\phi$-$(k,n)$-absorbing and $\phi$-$(k,n)$-absorbing primary hyperideals. Assume that $\phi$ is a function from $ \mathcal{HI}(R)$ to $\mathcal{HI}(R) \cup \{\varnothing\}$ such that $\mathcal{HI}(R)$ is the set of hyperideals of $R$ and $k$ is a positive integer. We call a proper hyperideal $Q$ of $R$ a $\phi$-$(k,n)$-absorbing (primary) hyperideal if for $r_1^{kn-k+1} \in R$, $g(r_1^{kn-k+1}) \in Q-\phi(Q)$ implies that there are $(k-1)n-k+2$ of the $r_i^,$s whose $g$-product is in $Q$ $\Bigl ($ $g(r_1^{(k-1)n-k+2}) \in Q$ or a $g$-product of $(k-1)n-k+2$ of $r_i^,$s ,except $g(r_1^{(k-1)n-k+2})$, is in $\boldsymbol{ r}^{(m,n)}(Q)$ $\Bigr )$. Several properties and characterizations of them are presented.