Adam Chapman

activity

20242026

collaborators

4 papers

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…

math.CO2024

Loops with involution and the Cayley-Dickson doubling process

Adam Chapman, Ilan Levin, Uzi Vishne +1

We develop a theory of loops with involution. On this basis we define a Cayley-Dickson doubling on loops, and use it to investigate the lattice of varieties of loops with involutio…

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

Loops with involution and the Cayley-Dickson doubling process

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