Resumen de On a problem by Nathan Jacobson

Victor Hugo López Solís, Ivan Shestakov

• We prove a coordinatization theorem for unital alternative algebras containing 2\times 22×2 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}H with the same 1, for the case when the algebra \mathbb{H}H is split. In particular, this is the case when the basic field is finite or algebraically closed.