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 2×22\times 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\mathbb{H} with the same 1, for the case when the algebra H\mathbb{H} 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