Localization, catenarity and dimensions in rings equipped with a Lie algebra action
type: Item
instance of: scholarly article
title: Localization, catenarity and dimensions in rings equipped with a Lie algebra action
zbMATH Open document ID: 0837.17004
author: T. Guédénon
published in: Journal of Algebra
publication date: 1996-05-21T00:00:00Z
review text: The objects of study in this paper are smash products \(R \# U ({\mathfrak g})\), where \(R\) is a Noetherian algebra, (often commutative), over a field \(k\) and \({\mathfrak g}\) is a (usually solvable or nilpotent) Lie algebra of finite dimension over \(k\) acting as derivations on \(R\). The topics treated include heights of prime ideals, catenarity, localisation of prime ideals, and homological conditions such as the finiteness of the global or injective dimensions of \(R \# U ({\mathfrak g})\). It is often necessary to assume that \({\mathfrak g}\) acts hypernormally or hypercentrally on \(R\). The results obtained generalise some well-known results for \(U ({\mathfrak g})\), and also the case of commuting derivations treated in [\textit{K. A. Brown}, \textit{K. R. Goodearl} and \textit{T. H. Lenagan}, Trans. Am. Math. Soc. 317, 749-772 (1990; Zbl 0692.16002)]. (Also submitted to M. R.).
Mathematics Subject Classification ID: 17B35
Mathematics Subject Classification ID: 16S40
Mathematics Subject Classification ID: 17B30
Mathematics Subject Classification ID: 16S32
Mathematics Subject Classification ID: 16P90
zbMATH DE Number: 826740
zbMATH Keywords: Lie algebra of derivations
zbMATH Keywords: global dimension
zbMATH Keywords: smash products
zbMATH Keywords: heights of prime ideals
zbMATH Keywords: catenarity
zbMATH Keywords: localisation of prime ideals
zbMATH Keywords: injective dimensions
Wikidata QID: Q115396145
reviewed by: Kenneth A. Brown
MaRDI profile type: Publication
full work available at URL: jabr.1995.1339
OpenAlex ID: W2001808297
DOI: 10.1006/JABR.1995.1339
description: scientific article; zbMATH DE number 826740