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LOCALIZATION AND CATENARITY IN ITERATED DIFFERENTIAL OPERATOR RINGS

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
    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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