Distributivity of certain lattices of varieties of associative rings (Q1070315)

Let \({\mathfrak M}\) be a variety of associative rings which satisfies the identity \(x^ 2-x^ 3f(x)=0\), f(x)\(\in {\mathbb{Z}}[x]\). The author proves that the lattice of subvarieties of \({\mathfrak M}\) is distributive. The proof uses the structure of finite critical rings.