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Let \(\mathcal {A}\) be an absolute-valued algebra with left-unit. For such an algebra, the two identities \((x^2, x^2, x)=0,\) \((x^2, x^2, x^2)=0\) are equivalent and give, in dimension 8,  four algebras. This allows to have a non-redundant list of all absolute-valued algebras with left unit satisfying \((x^2, x^2, x^r)=0\) .

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Absolute-Valued Algebras with Left-Unit Satisfying \((x^2, x^2, x^r)=0\) Revised

  • 会议论文

  • 发表日期：

    2026年

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  • Pape Aliou Dieng,
  • Alassane Diouf,
  • Abdellatif Rochdi

摘要

Let \(\mathcal {A}\) be an absolute-valued algebra with left-unit. For such an algebra, the two identities \((x^2, x^2, x)=0,\) \((x^2, x^2, x^2)=0\) are equivalent and give, in dimension 8,  four algebras. This allows to have a non-redundant list of all absolute-valued algebras with left unit satisfying \((x^2, x^2, x^r)=0\) .