superderivations and jordan superderivations of generalized quaternion algebras

Let h α, β. be the generalized quaternion algebra over a unitary commutative ring. this paper aims to consider superderivations and jordan superderivations of h α, β and hence to obtain the superalgebra der s (h α, β) of superderivations and der s (h α, β) of jordan superderivations of h α, β. it turns out that on generalized quaternion algebras, any superderivation is inner.  in particular, there exist jordan superderivations that are not superderivations.