On almost-free modules over complete discrete valuation rings
type: Item
instance of: scholarly article
title: On almost-free modules over complete discrete valuation rings
zbMATH Open document ID: 0756.13015
author: Rüdiger Göbel
author: B. Goldsmith
published in: Rendiconti del Seminario Matematico della Università di Padova
publication date: 1992-09-27T00:00:00Z
full work available at URL: http://www.numdam.org/item
full work available at URL: https://eudml.org/doc/108243
review text: Investigations on the behaviour of torsion-free reduced modules over complete discrete valuation rings have been previously carried out by these and other authors in ZFC set theory. In this paper similar investigations are made, working under the additional set-theoretical hypothesis \(V=L\). The modules involved here are strongly \(\chi\)-free quâ \(A\)-modules, where \(A\) is an algebra. The usual step-lemmas associated with a construction in \(V=L\) are derived and used in the proof of theorem 1, which maintains that if \(R\) is a complete discrete valuation ring and \(A\) is a unital, torsion-free, Hausdorff (in the \(p\)- adic topology) \(R\)-algebra, then, for each regular, not-weakly compact cardinal \(\chi>| A|\), there exists a strongly \(\chi\)-free \(A\)- module \(H\) of cardinality \(\chi\) such that \(E_ R(H)=A\otimes\text{Ines} H\). A second theorem is proved and is generalized in theorem 3, of which an indication of proof is given.
Mathematics Subject Classification ID: 13F30
Mathematics Subject Classification ID: 03E45
zbMATH DE Number: 60481
zbMATH Keywords: endomorphism
zbMATH Keywords: torsion-free modules
zbMATH Keywords: torsion-free reduced modules
zbMATH Keywords: complete discrete valuation rings
reviewed by: Frieda Theron
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 60481