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Cyclic Division Algebras of Odd Prime Degree are never Amitsur-Small (2508.07451v1)
Published 10 Aug 2025 in math.RA and math.AG
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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