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arXiv · 2508.07451

Cyclic Division Algebras of Odd Prime Degree are never Amitsur-Small

Adam Chapman·Ilan Levin·Marco Zaninelli
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Abstract

A division ring $D$ is Amitsur-Small if for every $n$ and every maximal left ideal $I$ in $D[x_1,\dots,x_n]$, $I \cap D[x_1,\dots,x_{n-1}]$ is maximal in $D[x_1,\dots,x_{n-1}]$. The goal of this note is to prove that cyclic division algebras of odd prime degree over their center are never Amitsur-Small.

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Adam Chapman, Ilan Levin, Marco Zaninelli. 2025-08-10. Cyclic Division Algebras of Odd Prime Degree are never Amitsur-Small. https://arxiv.org/abs/2508.07451

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