Self-projective modules over valuation rings
type: Item
instance of: scholarly article
title: Self-projective modules over valuation rings
zbMATH Open document ID: 0532.13003
DOI: 10.1007/BF01196656
author: Peter Herrmann
published in: Archiv der Mathematik
publication date: 1984-01-01T00:00:00Z
review text: Let R be a valuation domain. The valuation domains all of whose ideals are self-projective are characterized as the almost maximal valuation domains. Furthermore, it is shown that R is complete in its R-topology if and only if the quotient field of R is a self-projective R-module, which leads to a characterization of maximal valuation domains. In addition, the structure of self-projective torsion-free modules of finite rank over almost maximal valuation domains is given and several results on the self-projectivity of direct sums of uniserial modules over valuation domains were obtained.
Mathematics Subject Classification ID: 13A18
Mathematics Subject Classification ID: 13C05
Mathematics Subject Classification ID: 13C10
Mathematics Subject Classification ID: 13J10
Mathematics Subject Classification ID: 13C12
zbMATH DE Number: 3843877
zbMATH Keywords: self-projective modules
zbMATH Keywords: almost maximal valuation domains
zbMATH Keywords: complete valuation domain
zbMATH Keywords: torsion-free modules
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf01196656
OpenAlex ID: W2050982770
description: scientific article; zbMATH DE number 3843877