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arXiv · 2108.03306

A non-commutative Nullstellensatz

Zhengheng Bao·Zinovy Reichstein
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Abstract

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.

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Zhengheng Bao, Zinovy Reichstein. 2021-08-06. A non-commutative Nullstellensatz. https://arxiv.org/abs/2108.03306

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