On a problem by Nathan Jacobson

Solis V.H.L.; Shestakov I.P. · Revista Matematica Iberoamericana (2022) · DOI: 10.4171/rmi/1299

Resumen

We prove a coordinatization theorem for unital alternative algebras containing 2 × 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 H with the same 1, for the case when the algebra H is split. In particular, this is the case when the basic field is finite or algebraically closed.

Instituciones: Universidad Nacional Santiago Antúnez de Mayolo