Pythagorean Triples in Unification Theory of Nilpotent Rings

Authors:
Ruvim Lipyanski
Affiliations:
-
Venue:
FCT '01 Proceedings of the 13th International Symposium on Fundamentals of Computation Theory
Year:
2001

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Abstract

All solutions of Pythagorean equation (P-equation) x12+ x22 = x32in relatively free rings of varieties of n-nilpotent associative or associative-commutative rings (n=3,4) are described. In particular, it is shown that Pythagorean equation has no minimal and complete set of solutions in free rings of such varieties, so unification type of these varieties is nullary. This is also valid for the variety of associative-commutative 3 (or 4)-nilpotent rings of characteristic two.