In [31] Mikheev proved that every right alternative algebra has a natural (left) Bol algebra structure.
Observe that for [alpha] = id the ternary operation "(,,)" is precisely the one defined in [29] (see also [31], Remark 2) and that makes any right (or left) alternative algebra into a left Bol algebra.
Let (A, *) be a right alternative algebra. If one defines on A a ternary operation "(,,)" by
Also, in a right alternative algebra (A, *) (over a ground field of characteristic different from 2), the following identity holds [37]:
(ii) If (A, *) is a left alternative algebra, it is also possible to get a natural left Bol algebra structure on (A, *).
Next one proceeds as in Theorem 26 observing that a left alternative algebra is also Jordan-admissible (see [36], Theorem 2, for right alternative algebras).
Maltsev algebras were introduced by Maltsev [7] in a study of commutator algebras of alternative algebras and also as a study of tangent algebras to local smooth Moufang loops.
Alternative algebras, Maltsev algebras, and Lts (among other algebras) received a twisted generalization in the development of the theory of Hom-algebras during these latest years.