The unification type of the Pythagorean equation in varieties of nilpotent rings

The unification type of the Pythagorean equation in relatively free rings of varieties of n-nilpotent associative or commutative–associative rings is described (n>2). It is shown that the Pythagorean equation has no minimal set of solutions in free rings of such varieties. This implies that the unification type of these varieties is nullary. We show also that the variety of associative or commutative–associative nilpotent rings of characteristic 2 has nullary unification type.