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TitleThe unification type of the Pythagorean equation in varieties of nilpotent rings
Author(s) G. Belitskii, R. Lipyanski
TypeArticle in Journal
AbstractThe 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 commutativeľassociative 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 commutativeľassociative nilpotent rings of characteristic 2 has nullary unification type.
KeywordsUnification theory, Nilpotent ring, Pythagorean equation
ISSN0747-7171
URL http://www.sciencedirect.com/science/article/pii/S0747717105001264
LanguageEnglish
JournalJournal of Symbolic Computation
Volume41
Number1
Pages67 - 79
Year2006
Edition0
Translation No
Refereed No
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