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Main Authors: Chapman, Adam, Levin, Ilan, Zaninelli, Marco
Format: Preprint
Published: 2025
Subjects:
Online Access:https://arxiv.org/abs/2508.07451
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author Chapman, Adam
Levin, Ilan
Zaninelli, Marco
author_facet Chapman, Adam
Levin, Ilan
Zaninelli, Marco
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2508_07451
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Cyclic Division Algebras of Odd Prime Degree are never Amitsur-Small
Chapman, Adam
Levin, Ilan
Zaninelli, Marco
Rings and Algebras
Algebraic Geometry
16K20, 16D25
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.
title Cyclic Division Algebras of Odd Prime Degree are never Amitsur-Small
topic Rings and Algebras
Algebraic Geometry
16K20, 16D25
url https://arxiv.org/abs/2508.07451