On a problem by Nathan Jacobson

  • Victor Hugo López Solís

    Universidad Nacional Santiago Antúnez de Mayolo, Huaraz, Peru
  • Ivan P. Shestakov

    Universidade de São Paulo, Brazil
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We prove a coordinatization theorem for unital alternative algebras containing 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 with the same 1, for the case when the algebra is split. In particular, this is the case when the basic field is finite or algebraically closed.

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Victor Hugo López Solís, Ivan P. Shestakov, On a problem by Nathan Jacobson. Rev. Mat. Iberoam. 38 (2022), no. 4, pp. 1219–1238

DOI 10.4171/RMI/1299