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 -> 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 = R is the field of real numbers and D is the algebra of IIamilton quaternions, it reduces to the quaternionic Nullstellensatz recently proved by Alon and Paran.
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