On the extension of derivations to some closures
type: Item
instance of: scholarly article
title: On the extension of derivations to some closures
zbMATH Open document ID: 0782.13008
author: Silvia Molinelli
author: Grazia Tamone
published in: Rocky Mountain Journal of Mathematics
publication date: 1993-06-29T00:00:00Z
review text: Soient \(A \subset B\) une extension d'anneaux noethérien et \(D=(1,D_ 1,\ldots,D_ i,\ldots)\) une dérivation de \(A\). On donne des conditions dans lesquelles il existe une extension de \(D\) pour un anneau \(C\) tel que \(A\subseteq C\subseteq B\). Si \(A\) et \(B\) sont des anneaux intègres on démontre qu'il existe une telle extension pour \(u\)-fermeture, \(t\)- fermeture, \(F\)-fermeture et \((n\)-root)-fermeture de \(A\) dans \(B\). Si \(B\) est la fermeture integrale de \(A\) dans son anneau total des fractions, on donne des conditions dans lesquelles il existe une extension de \(D\) pour les anneau de la forme \(A^ \Delta\), où \(\Delta\) soit un système multiplicatif des ideaux de \(A\) non nuls.
reviewed by: Nicolae Radu
Mathematics Subject Classification ID: 13B10
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13N05
zbMATH DE Number: 219346
zbMATH Keywords: extension of noetherian rings
zbMATH Keywords: extension of derivation
zbMATH Keywords: integral closure
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181072667
OpenAlex ID: W2047910208
cites work: Seminormality in power series rings
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cites work: Q3693593
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DOI: 10.1216/RMJM/1181072667
description: scientific article; zbMATH DE number 219346