A non-commutative Nullstellensatz

Let [Formula: see text] be a field and finite-dimensional central division algebra over text]. We prove variant of the Nullstellensatz for text]-sided ideals in ring polynomial maps In case where is commutative, our main result reduces to text]-Nullstellensatz Laksov Adkins–Gianni–Tognoli. case, real numbers Hamilton quaternions, it quaternionic recently proved by Alon Paran.