A full description is provided for bicommutative algebra varieties over char-0 fields obeying a cubic identity, together with a criterion for when their subvariety lattice is distributive.
Drensky, On the identities of the three-dimensional simple Jordan algebra, Annuaire Univ
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Varieties of bicommutative algebras with identity of degree three
A full description is provided for bicommutative algebra varieties over char-0 fields obeying a cubic identity, together with a criterion for when their subvariety lattice is distributive.