Reductive derivations of local rings of characteristic p
type: Item
instance of: scholarly article
title: Reductive derivations of local rings of characteristic p
zbMATH Open document ID: 0624.13006
DOI: 10.1016/0021-8693(87)90146-3
author: Annetta G. Aramova
published in: Journal of Algebra
publication date: 1987-01-01T00:00:00Z
review text: Let A be a commutative noetherian algebra over the field with p elements. A notion of reductive derivations \(d: A\to A\) is introduced in terms of rings of differential operators. In particular, the semisimple derivations are reductive. It is shown that for an arbitrary derivation of a local ring, the study of its constants may be reduced to the case when the derivation maps the ring into its maximal ideal. Moreover, if the original derivation is reductive, the modified one is semisimple. It is proved that the rings of constants of reductive derivations inherit the Buchsbaum and the Cohen-Macaulay properties. The Gorenstein descent is investigated. A Hinič character of a semisimple derivation is defined and the canonical module of the ring of constants is described in terms of it.
Mathematics Subject Classification ID: 13B10
Mathematics Subject Classification ID: 13H99
Mathematics Subject Classification ID: 13N05
zbMATH DE Number: 4012772
zbMATH Keywords: Cohen-Macaulay ring
zbMATH Keywords: reductive derivations
zbMATH Keywords: rings of differential operators
zbMATH Keywords: Buchsbaum
zbMATH Keywords: Gorenstein descent
zbMATH Keywords: Hinič character
zbMATH Keywords: canonical module of the ring of constants
reviewed by: E. V. Pankrat'ev
MaRDI profile type: Publication
full work available at URL: 0021-8693(87)90146-3
OpenAlex ID: W2044912045
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description: scientific article; zbMATH DE number 4012772