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T. Guédénon 《代数通讯》2013,41(8):2781-2793
The objective of this article is the study of localization and catenarity in strongly G-graded rings with Noetherian base ring, where G is a finitely generated, nilpotent and torsionfree group. We generalize some results of Guédénon (2000). It follows from Corollary 2.6 that if G is free Abelian of finite rank and A is a commutative strongly G-graded ring with base ring a Noetherian regular integral domain, then A is a Noetherian regular integral domain. 相似文献
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T. Guédénon 《代数通讯》2013,41(12):4403-4413
ABSTRACT Let k be a field, R an associative k-algebra with identity, Δ a finite set of derivations of R, and R[Θ1, δ1] ··· [Θ n , δ n ] an iterated differential operator k-algebra over R such that δ j (Θ i ) ∈ R[Θ1, δ1] ··· [Θ i?1, δ i?1]; 1 ≤ i < j ≤ n. If R is Noetherian Δ-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 Δ-prime ideals of R, the local ring A P is regular in the sense of Robert Walker. We use this result to study the catenarity of A and to compute the numbers μ 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. 相似文献
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