Adam Chapman

most citedLoops with involution and the Cayley-Dickson doubling process

1 citations · 1 across the 4 of their papers we have counts for

collaborators

5 papers

math.RA2025

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.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.RA2025

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.CO2024★ 1 cited

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…

math.KT2024

Invariant for Sets of Pfister Forms

Adam Chapman, Ilan Levin

We associate an $(n_{1} + \dots + n_{t} - k (t - 1))$ -fold Pfister form to any $t$ -tuple of $k$ -linked Pfister forms of dimensions $2^{n_{1}}, \dots, 2^{n_{t}}$ , and prove its invariance under the di…

Essential Dimension of Central Simple Algebras when the Characteristic is Bad

The Cyclicity of Tensor Products of Cyclic p-Algebras

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

Loops with involution and the Cayley-Dickson doubling process

Invariant for Sets of Pfister Forms

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