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.
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}
}