Pairs of integral domains with most of the intermediate rings PVD
type: Item
instance of: scholarly article
title: Pairs of integral domains with most of the intermediate rings PVD
zbMATH Open document ID: 1390.13027
author: Noômen Jarboui
author: Salma Trabelsi
published in: Ricerche di Matematica
publication date: 2017-12-01T00:00:00Z
review text: A PVD is a pseudo-valuation domain, i.e. a ring \(R\) such that there is a valuation ring \(V\) with \(R\subset V\subset \text{Frac}(R)\) and Spec\((R)=\) Spec\((V)\). The main result of the paper under review is that, given an extension of integral domains \(R\subset S\), if every proper subring of \(S\) containing \(R\) is a PVD then \(S\) is a PVD. From this the authors deduce that, given an extension of integral domains \(R\subset S\), if every proper subring of \(S\) containing \(R\) is a valuation domain (resp. a DVR) then \(S\) is a also a valuation domain (resp. the quotient field of \(R\)).
reviewed by: Guillaume Rond
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13A18
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13B25
Mathematics Subject Classification ID: 13C13
zbMATH DE Number: 6815066
zbMATH Keywords: integral domain
zbMATH Keywords: intermediate ring
zbMATH Keywords: overring
zbMATH Keywords: ring extension
zbMATH Keywords: integral extension
zbMATH Keywords: integrally closed
zbMATH Keywords: Prüfer domain
zbMATH Keywords: valuation domain
zbMATH Keywords: discrete valuation domain
MaRDI profile type: Publication
full work available at URL: s11587-016-0310-z
OpenAlex ID: W2543787515
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DOI: 10.1007/S11587-016-0310-Z
description: scientific article; zbMATH DE number 6815066