On a problem by Nathan Jacobson
Victor Hugo López SolísUniversidad Nacional Santiago Antúnez de Mayolo, Huaraz, Peru
Ivan P. ShestakovUniversidade de São Paulo, Brazil
We prove a coordinatization theorem for unital alternative algebras containing 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 with the same 1, for the case when the algebra 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. 1219–1238DOI 10.4171/RMI/1299