Geodesic
Linearly minimal Jordan algebras of characteristic other than~2
Algebra i logika, Tome 54 (2015) no. 6, pp. 653-662.

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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.
Keywords: Jordan algebra, division algebra, field. 
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E. R. Baisalov; A. Aljouiee. Linearly minimal Jordan algebras of characteristic other than~2. Algebra i logika, Tome 54 (2015) no. 6, pp. 653-662. http://geodesic.mathdoc.fr/item/AL_2015_54_6_a0/

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