The unification type of the Pythagorean equation in varieties of nilpotent rings Academic Article uri icon

abstract

  • The unification type of the Pythagorean equation x 1 2 + x 2 2 = x 3 2 in relatively free rings of varieties of n -nilpotent associative or commutative‚Äďassociative 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‚Äďassociative nilpotent rings of characteristic 2 has nullary unification type.

publication date

  • January 1, 2006