On subquasivariety lattices of semi-primal varieties (Q2266036)

It is well known that the subvariety lattice of a semi-primal variety is distributive. In the present note the author constructs a sequence \(\{A_ n\}\) of semi-primal algebras with the following property: Let \(Q(A_ n)\) be the subquasivariety lattice of the variety generated by \(A_ n\). It is shown there is no non-trivial lattice identity which holds in all of the \(Q(A_ n)\), and hence there is no non-trivial lattice identity which holds in all subquasivariety lattices of semi- primal algebras.