On a problem by Nathan Jacobson

• Victor Hugo López Solís ^[1] ; Ivan P. Shestakov ^[2]
  1. [1] Universidad Nacional Santiago Antúnez de Mayolo

     Universidad Nacional Santiago Antúnez de Mayolo

     Huaraz, Perú

     
  2. [2] Universidade de São Paulo

     Universidade de São Paulo

     Brasil

     
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 38, Nº 4, 2022, págs. 1219-1238
• Idioma: inglés
• DOI: 10.4171/RMI/1299
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• Resumen

  • 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.