  In 1981, S. V. Pchelintsev introduced the notion of topological rank for
Spechtian varieties of algebras as a certain tool for studying the structure of
non-nilpotent subvarieties in a given variety. We provide a variety of right
alternative algebras of arbitrary given finite topological rank. Namely, we
prove that the topological rank of the variety of right alternative metabelian
(solvable of index two) algebras that are Lie-nilpotent of step not more than
$s$ over a field of characteristic distinct from two and three is equal to $s$.
