Title | **The unification type of the Pythagorean equation in varieties of nilpotent rings** |

Author(s) | G. Belitskii, R. Lipyanski |

Type | Article in Journal |

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–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. |

Keywords | Unification theory, Nilpotent ring, Pythagorean equation |

ISSN | 0747-7171 |

URL |
http://www.sciencedirect.com/science/article/pii/S0747717105001264 |

Language | English |

Journal | Journal of Symbolic Computation |

Volume | 41 |

Number | 1 |

Pages | 67 - 79 |

Year | 2006 |

Edition | 0 |

Translation |
No |

Refereed |
No |