A note on maximal non-Noetherian subrings of a domain
type: Item
instance of: scholarly article
title: A note on maximal non-Noetherian subrings of a domain
zbMATH Open document ID: 1237.13019
author: Noômen Jarboui
author: Ayada Jerbi
published in: Beiträge zur Algebra und Geometrie
publication date: 2012-02-29T00:00:00Z
review text: A domain \(R\) is said to be an S(=Seidenberg)-domain if each height one prime ideal \(P \subset R\) extends to a height one prime ideal \(P[X] \subset R[X]\), where \(R[X]\) denotes the polynomial ring in one variable \(X\) over \(R\). A domain \(R\) is called a strong S-domain if \(R/P\) is an S-domain for each prime ideal \(P \subset R\). A domain \(R\) is called stably strong S-domain provided the polynominal ring \(R[X_1,\ldots,X_n]\) is a strong S-domain for any \(n \geq 1\). In the paper it is shown: If \(R\) is a maximal non-Noetherian subring of \(S\) then \(R\) is a stably strong S-domain and that \(R\) is universally catenerian if and only if \(S\) is universally catenerian. The results lead to new examples of stably strong S-domains and universally catenarian domains. The relationship with \(n\)-dimensional pairs and residually Mori pairs is also investigated.
reviewed by: Peter Schenzel
Mathematics Subject Classification ID: 13B02
Mathematics Subject Classification ID: 13A15
Mathematics Subject Classification ID: 13A18
Mathematics Subject Classification ID: 13B21
Mathematics Subject Classification ID: 13B22
Mathematics Subject Classification ID: 13B30
Mathematics Subject Classification ID: 13C15
Mathematics Subject Classification ID: 13E05
zbMATH DE Number: 6010043
zbMATH Keywords: Seidenberg domain
zbMATH Keywords: universally catenerian
zbMATH Keywords: stably strong Seidenberg domain
MaRDI profile type: Publication
full work available at URL: s13366-011-0055-5
OpenAlex ID: W2089178673
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DOI: 10.1007/S13366-011-0055-5
description: scientific article; zbMATH DE number 6010043