### Infinite independent systems of identities of alternative commutative algebra over a field of characteristic three

Let 𝔄₃ denote the variety of alternative commutative (Jordan) algebras defined by the identity x³ = 0, and let 𝔖₂ be the subvariety of the variety 𝔄₃ of solvable algebras of solviability index 2. We present an infinite independent system of identities in the variety 𝔄₃ ∩ 𝔖₂𝔖₂. Therefore we infer that 𝔄₃ ∩ 𝔖₂𝔖₂ contains a continuum of infinite based subvarieties and that there exist algebras with an unsolvable words problem in 𝔄₃ ∩ 𝔖₂𝔖₂. It is worth mentioning that these results were...