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.