Boolean families of valuation rings. II
type: Item
instance of: scholarly article
title: Boolean families of valuation rings. II
zbMATH Open document ID: 0824.12004
DOI: 10.1007/BF02261692
published in: Algebra and Logic
publication date: 1995-04-20T00:00:00Z
review text: The aim of the paper is to strengthen the author's earlier results [Algebra Logic 31, No. 3, 170-181 (1992); translation from Algebra Logika 31, No. 3, 276-296 (1992; Zbl 0791.12004)]. It is shown that if \(W\) is a weakly Boolean family of valuation rings of a field \(F\) and \(R= R_ W \rightleftharpoons \cap \{R_ V\mid R_ V\in W\}\) is a Prüfer ring with field of quotients \(F\), then \(W\) is Boolean. It is a considerably stronger version of proposition 4 of the above-cited paper. Sufficient conditions for a family of valuation rings of a field to be Boolean are formulated. It is proved that every regular Prüfer ring is a Bezout ring.
Mathematics Subject Classification ID: 12J10
Mathematics Subject Classification ID: 54G99
zbMATH DE Number: 738948
zbMATH Keywords: weakly Boolean family of valuation rings
zbMATH Keywords: Prüfer ring
zbMATH Keywords: Bezout ring
author: Yuri L. Ershov
MaRDI profile type: Publication
cites work: Boolean families of valuation rings
cites work: Principal ideal theorems for holomorphy rings in fields.
full work available at URL: https://doi.org/10.1007/bf02261692
OpenAlex ID: W4255142616
description: scientific article; zbMATH DE number 738948