2020/07/18 by Victor Hugo López Solís, I. P. Shestakov, Solís, Victor H. López +1 · 1 citation
Mathematics · Computer Science · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Matrix Theory and Algorithms
paper · pdf · doi:10.48550/arxiv.2007.09313
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.