Adam Chapman

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20242026

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math.RA2026

Essential Dimension of Central Simple Algebras when the Characteristic is Bad

Adam Chapman, Kelly McKinnie

This is a survey of the existing literature, the state of the art, and a few minor new results and open questions regarding the essential dimension of central simple algebras and f…

math.RA2026

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

Adam Chapman, Ilan Levin, Marco Zaninelli

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 $D [x_{1}, \dots, x_{n - 1}]$ . Th…

math.RA2025

The Cyclicity of Tensor Products of Cyclic $p$ -Algebras

Adam Chapman

We revisit the famous theorem of Albert's on the cyclicity of tensor products of cyclic $p$ -algebras. In the case of tensor products of cyclic $p$ -algebras of prime degree, we prov…

Essential Dimension of Central Simple Algebras when the Characteristic is Bad

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

The Cyclicity of Tensor Products of Cyclic p-Algebras

The Cyclicity of Tensor Products of Cyclic $p$ -Algebras