On the sumsets of exceptional units in quaternion rings

We investigate sums of exceptional units in a quaternion ring $H(R)$ over a finite commutative ring R. We prove that in order to find the number of representations of an element in $H(R)$ as a sum of k exceptional units for some integer k ≥ 2, we can limit ourselves to studying the quaternion rings over local rings. For a local ring R of even order, we find the number of representations of an element of $H(R)$ as a sum of k exceptional units for any integer k ≥ 2. For a local ring R of odd order, we find either the number or the bounds for the number of representations of an element of $H(R)$ as a sum of $2$ exceptional units.