  Let $K$ be a field and $D$ be a finite-dimensional central division algebra
over $K$. We prove a variant of the Nullstellensatz for $2$-sided ideals in the
ring of polynomial maps $D^n \to D$. In the case where $D = K$ is commutative,
our main result reduces to the $K$-Nullstellensatz of Laksov and
Adkins-Gianni-Tognoli. In the case, where $K = \mathbb R$ is the field of real
numbers and $D$ is the algebra of Hamilton quaternions, it reduces to the
quaternionic Nullstellensatz recently proved by Alon and Paran.
