A note on locally noetherian pairs
type: Item
instance of: scholarly article
title: A note on locally noetherian pairs
zbMATH Open document ID: 0541.13006
author: Ravinder Kumar
published in: Journal of Mathematics of Kyoto University
publication date: 1983-01-01T00:00:00Z
review text: The pair (A,B) of domains is called a ''Noetherian pair'' (N.P.) if \(A\subseteq B\) and all the rings intermediate between A and B are Noetherian [\textit{A. R. Wadsworth}, Trans. Am. Math. Soc. 195, 201-211 (1974; Zbl 0294.13010)]. The present author defines a ''locally Noetherian pair'' to be a pair \(A\subseteq B\) of domains such that \((A_{{\mathfrak m}},B\otimes_ AA_{{\mathfrak m}})\) is an N.P. for all maximal ideals \({\mathfrak m}\) of A. He gives some classes of examples of locally N.P. rings which are not N.P., and extends some of Wardsworth's results to the more general setting.
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 13B02
zbMATH DE Number: 3859267
reviewed by: Kenneth A. Brown
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1215/kjm/1250521428
OpenAlex ID: W1577094793
DOI: 10.1215/KJM/1250521428
description: scientific article; zbMATH DE number 3859267