It is proved that every nontrivial linearly minimal Jordan algebra of characteristic other than 2 is a division algebra. Then Zel’manov’s classification of Jordan division algebras is applied to show that such an algebra is a field.
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(E. R. Baisalov) Supported by the Deanship of Scientific Research of the Imam Muhammad ibn Saud Islamic University, grant ID 341207 1433.
(E. R. Baisalov) Supported by KN MON RK, grant No. 3953/GF 4 (2015–2017).
Translated from Algebra i Logika, Vol. 54, No. 6, pp. 653–662, November-December, 2015.
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Baisalov, E.R., Al’dzhuie, A. Linearly Minimal Jordan Algebras of Characteristic Other Than 2. Algebra Logic 54, 421–427 (2016). https://doi.org/10.1007/s10469-016-9364-y
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DOI: https://doi.org/10.1007/s10469-016-9364-y