strongly weak idempotent nil -clean rings

We introduce the concept of strongly weak idempotent nil-clean rings which is a generalization of strongly weakly nil clean rings. we characterize strongly weak idempotent nil-clean rings in terms of the set of nilpotent elements, homomorphic images, and jacobson radicals. we prove that a ring $r$ is strongly weak idempotent nil-clean if and only if for any $ain r$, $a-a^3$ is nilpotent if and only if $nil(r)$ forms an ideal and $r/{nil(r)}$ is reduced weak idempotent nil-clean if and only if $r$ has no homomorphic image $mathbb{z}_3oplus mathbb{z}_3$ and $a^2-a^4$ is nilpotent. moreover, we prove that a strongly weak idempotent nil-clean ring $r$ with $2in j(r)$ satisfies nil-involution property.