Differential modules with maximal torsion
type: Item
instance of: scholarly article
title: Differential modules with maximal torsion
zbMATH Open document ID: 0780.13015
DOI: 10.1007/BF01246740
author: Thomas Pohl
published in: Archiv der Mathematik
publication date: 1993-02-18T00:00:00Z
review text: Let \(R\) be a reduced local analytic \(k\)-algebra, where \(k\) is a field of characteristic zero. It is well known that \(R\) is regular iff its universally finite differential module \(D(R/k)\) is free. A still unsettled conjecture of \textit{R. Berger} [Math. Z. 81, 326-354 (1963; Zbl 0113.263)] states that if \(R\) is one-dimensional then \(R\) is regular if \(D(R/k)\) is torsionfree. The main result of this paper states that Berger's conjecture is true in case \(RDR=DR\) [theorem 3]. This condition is satisfied, e.g., if \(D(R/k)\) has maximal torsion.
Mathematics Subject Classification ID: 13J07
Mathematics Subject Classification ID: 13N05
zbMATH DE Number: 124274
zbMATH Keywords: Berger's conjecture
zbMATH Keywords: reduced local analytic algebra
zbMATH Keywords: differential module
reviewed by: Karl-Heinz Kiyek
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 124274