$J$-hyperideals and their expansions in a Krasner $(m,n)$-hyperring

Over the years, different types of hyperideals have been introduced in order to let us fully realize structures hyperrings general. The aim this research work is define and characterize a new class Krasner $(m,n)$-hyperring that we call n-ary $J$-hyperideals. A proper hyperideal $Q$ with scalar identity $1_R$ said be an $J$-hyperideal if whenever $x_1^n \in R$ such $g(x_1^n) Q$ $x_i \notin J_{(m,n)}(R)$, then $g(x_1^{i-1},1_R,x_{i+1}^n) Q$. Also, study concept $\delta$-$J$-hyperideals as expansion Finally, extend notion $(k,n)$-absorbing $\delta$-$J$-hyperideals. Let $\delta$ $R$ $k$ positive integer. called $\delta$-$J$-hyperideal for $x_1^{kn-k+1} R$, $g(x_1^{kn-k+1}) implies $g(x_1^{(k-1)n-k+2}) J_{(m,n)}(R)$ or $g$-product $(k-1)n-k+2$ $x_i^,$ s except $g(x_1^{(k-1)n-k+2})$ $\delta(Q)$.