# On a problem by Nathan Jacobson

### Victor Hugo López Solís

Universidad Nacional Santiago Antúnez de Mayolo, Huaraz, Peru### Ivan P. Shestakov

Universidade de São Paulo, Brazil

## Abstract

We prove a coordinatization theorem for unital alternative algebras containing $2\times 2$ matrix algebra with the same identity element 1. This solves an old problem announced by Nathan Jacobson on the description of alternative algebras containing a generalized quaternion algebra $\mathbb{H}$ with the same 1, for the case when the algebra $\mathbb{H}$ is split. In particular, this is the case when the basic field is finite or algebraically closed.

## Cite this article

Victor Hugo López Solís, Ivan P. Shestakov, On a problem by Nathan Jacobson. Rev. Mat. Iberoam. 38 (2022), no. 4, pp. 1219–1238

DOI 10.4171/RMI/1299