On topologies over rings
type: Item
instance of: scholarly article
title: On topologies over rings
zbMATH Open document ID: 0574.16028
DOI: 10.1155/S0161171285000217
author: Syed M. Fakhruddin
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1985-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/45969
review text: The paper deals with the topological rings which have bases of neighbourhoods of zero consisting of right ideals. A topology \({\mathcal T}\) on the ring R is called a Gabriel topology if it satisfies the condition: if \({\mathcal I}\subset {\mathcal J}\), where \({\mathcal I}\) and \({\mathcal J}\) are right ideals in R, \({\mathcal J}\in {\mathcal T}\) and (\({\mathcal I}:a)\in {\mathcal T}\) for every \(a\in {\mathcal J}\), then \({\mathcal I}\in {\mathcal T}\). The author partially answers the question concerning the description of the smallest Gabriel topology \({\mathcal T}'\) which contains the topology \({\mathcal T}\). The result obtained by the author includes the case of right Noetherian rings.
Mathematics Subject Classification ID: 16W80
Mathematics Subject Classification ID: 16Dxx
Mathematics Subject Classification ID: 16S90
zbMATH DE Number: 3916510
zbMATH Keywords: topological rings
zbMATH Keywords: right ideals
zbMATH Keywords: Gabriel topology
reviewed by: Mihail I. Ursul
MaRDI profile type: Publication
OpenAlex ID: W2044787362
description: scientific article; zbMATH DE number 3916510