Differential simplicity and the module of derivations
type: Item
instance of: scholarly article
title: Differential simplicity and the module of derivations
zbMATH Open document ID: 0876.13012
DOI: 10.1016/S0022-4049(96)00003-5
author: Alok Kumar Maloo
published in: Journal of Pure and Applied Algebra
publication date: 1997-03-05T00:00:00Z
review text: Let \(A\) be a Noetherian local ring and \(D\subset \text{Der} (A)\) a finitely generated \(A\)-submodule, which is closed under Lie operation of derivations. If \(I\) is a maximally \(D\)-differential ideal then \(D/ID\) is free over \(A/I\). In particular, if \(A\) contains a field \(k\) such that \(D= \text{Der}_k (A)\) is finitely generated over \(A\) and \(A\) is differentially simple under \(D\) then \(D\) is free over \(A\).
Mathematics Subject Classification ID: 13N05
Mathematics Subject Classification ID: 13B10
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 986726
zbMATH Keywords: differential ideal
zbMATH Keywords: derivations
MaRDI profile type: Publication
cites work: Constructing bad Noetherian local domains using derivations
cites work: Derivations on Commutative Rings
cites work: Differential simplicity and complete integral closure
cites work: Maximally differential ideals
cites work: Q3739243
cites work: Maximally differential prime ideals in a complete local ring
cites work: Studies in Equisingularity I Equivalent Singularities of Plane Algebroid Curves
Wikidata QID: Q127498926
full work available at URL: s0022-4049(96)00003-5
OpenAlex ID: W2081832909
description: scientific article; zbMATH DE number 986726