Title | **A finiteness condition for algebras over coordinate rings of varieties** |

Author(s) | Adam Hajduk, Stanisław Kasjan |

Type | Article in Journal |

Abstract | Let A be a finitely presented k [ X ] -algebra, where k [ X ] is the algebra of regular functions on a variety X defined over an algebraically closed field k . The following problem arises in the study of degenerations of algebras (Hajduk and Kasjan, in press [7]). Assume that the specialization of A at x has finite dimension over k for every x from a dense subset of X . Is there an open dense subset U of X such that the localization of A with respect to U is a finitely generated k [ U ] -module? We prove that this is the case if k has infinite transcendence degree over its prime subfield. We provide some applications to the concept of generalized CB-degenerations. |

ISSN | 0022-4049 |

URL |
http://www.sciencedirect.com/science/article/pii/S0022404912002034 |

Language | English |

Journal | Journal of Pure and Applied Algebra |

Volume | 217 |

Number | 1 |

Pages | 190 - 194 |

Year | 2013 |

Edition | 0 |

Translation |
No |

Refereed |
No |