English

On a problem by Nathan Jacobson

Rings and Algebras 2020-07-21 v1

Abstract

We prove a coordinatization theorem for unital alternative algebras containing 2 x 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.

Keywords

Cite

@article{arxiv.2007.09313,
  title  = {On a problem by Nathan Jacobson},
  author = {Victor H. López Solís and Ivan P. Shestakov},
  journal= {arXiv preprint arXiv:2007.09313},
  year   = {2020}
}
R2 v1 2026-06-23T17:12:42.267Z