Guédénon, Thomas (2005) *LOCALIZATION AND CATENARITY IN ITERATED DIFFERENTIAL OPERATOR RINGS.* [Electronic Journal]

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## Abstract

Let k be a field, R an associative k-algebra with identity, \delta a finite set of derivations of R, and R[\theta_1, \sigma_1] ... R[\theta_n, \sigma_n] an iterated differential operator k-algebra over R such that \sigma_j(\theta_j) \in R[\theta_{i-1}, \sigma_{i-1}] ... R[\theta_n, \sigma_n] 1 ≤ i < j ≤ n. If R is Noetherian \delta hypercentral, then every prime ideal P of A is classically localizable. The aim of this article is to show that under some additional hypotheses on the \delta-prime ideals of R, the local ring AP is regular in the sense of Robert Walker. We use this result to study the catenarity of A and to compute the numbers i of Bass. Let g be a nilpotent Lie algebra of finite dimension n acting on R by derivations and U(g) the enveloping algebra of g. Then the crossed product of R by U(g) is an iterated differential operator k-algebra as above. In this particular case, our results are known if k has characteristic zero.

Item Type: | Electronic Journal |
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Additional Information: | pubdom TRUE |

Uncontrolled Keywords: | AR property; Catenarity; Classical Krull dimension; Classically localizable prime ideals; Crossed products; Derivations; Differential operator rings; Height of a prime ideal; Homological dimensions; Invariant of Bass; Krull dimension; Lie algebra; Noetherian rings; Regular local rings; AARMS. |

Subjects: | 16-xx Associative rings and algebras 17-xx Nonassociative rings and algebras |

Faculty: | UNSPECIFIED |

Depositing User: | lingyun ye |

Date Deposited: | 09 Jul 2007 |

Last Modified: | 27 Apr 2010 16:32 |

URI: | https://docserver.carma.newcastle.edu.au/id/eprint/349 |

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