A direct proof of a theorem concerning treed overrings
type: Item
instance of: scholarly article
title: A direct proof of a theorem concerning treed overrings
zbMATH Open document ID: 1441.13018
DOI: 10.1155/2015/938648
author: Ahmed Ayache
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2018-05-25T00:00:00Z
review text: Summary: We improve and provide a direct proof of a theorem that answered a question by Dobbs about treed overrings. More precisely, we show that if \(R\) is an integrally closed local domain and each of its \textit{proper} overrings is treed, then \(R\) is a valuation domain or \(R\) is a PVD with associated valuation overring \(V\) such that \(\mathrm{tr.deg} [V / M : R / M] = 1\).
Mathematics Subject Classification ID: 13B02
zbMATH DE Number: 6873273
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2015/938648
OpenAlex ID: W1497983224
cites work: Q4732550
cites work: On Going Down For Simple Overrings II
cites work: Q4163618
cites work: Simple Going Down
cites work: Pseudo-valuation domains
cites work: Q3205350
cites work: Pairs of Rings with the Same Prime Ideals
cites work: An answer to a Dobbs conjecture about treed domains
cites work: Integrally closed domains with treed overrings
cites work: Q5661989
cites work: Construction B, I, D et anneaux localement ou residuellement de Jaffard. (B, I, D construction and locally or residually Jaffard rings)
cites work: Q3931518
cites work: Q3992268
cites work: Topologically defined classes of commutative rings
Wikidata QID: Q59109874
DBLP publication ID: journals/ijmmsc/Ayache15
description: scientific article; zbMATH DE number 6873273