Noetherian property of inductive limits of Noetherian local rings
type: Item
instance of: scholarly article
title: Noetherian property of inductive limits of Noetherian local rings
zbMATH Open document ID: 0743.13010
author: Tetsushi Ogoma
published in: Proceedings of the Japan Academy. Series A
publication date: 1992-06-27T00:00:00Z
review text: This note is concerned with verifying the following result. Let \(\{(A_ i,m_ i)\mid i\) is an element of \(I\)\} be a filtered inductive system of noetherian local rings such that \(m_ iA_ j=m_ j\) for \(j\geq i\). Then the inductive limit \(A\) of the system is noetherian.
Mathematics Subject Classification ID: 13E05
Mathematics Subject Classification ID: 18A30
Mathematics Subject Classification ID: 13H99
zbMATH DE Number: 29819
zbMATH Keywords: noetherianness
zbMATH Keywords: filtered inductive system
zbMATH Keywords: inductive limit
reviewed by: Ann K. Boyle
MaRDI profile type: Publication
full work available at URL: pjaa.67.68
OpenAlex ID: W2027523853
cites work: Q5735274
cites work: Q3863985
DOI: 10.3792/PJAA.67.68
description: scientific article; zbMATH DE number 29819