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

G. Belitskii; R. Lipyanski

doi:10.1016/j.jsc.2005.09.002

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

G. Belitskii, R. Lipyanski

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

The unification type of the Pythagorean equation x₁² + x₂² = x₃² 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.

Original language	English
Pages (from-to)	67-79
Number of pages	13
Journal	Journal of Symbolic Computation
Volume	41
Issue number	1
DOIs	https://doi.org/10.1016/j.jsc.2005.09.002
State	Published - 1 Jan 2006

Keywords

Nilpotent ring
Pythagorean equation
Unification theory

ASJC Scopus subject areas

Algebra and Number Theory
Computational Mathematics

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10.1016/j.jsc.2005.09.002

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abstract = "The unification type of the Pythagorean equation x12 + x22 = x32 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.",

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AB - The unification type of the Pythagorean equation x12 + x22 = x32 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.

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KW - Unification theory

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

Abstract

Keywords

ASJC Scopus subject areas

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