The canonical topology of certain rings
type: Item
instance of: scholarly article
title: The canonical topology of certain rings
zbMATH Open document ID: 0594.16025
published in: Bulletin of the Iranian Mathematical Society
publication date: 1984-01-01T00:00:00Z
review text: Let R be a ring with 1, \(E_ 0\) the injective envelope of the left module \({}_ RR\), \(E_ 1\) the injective envelope of \(E_ 0/R\) and let \(F^ 1_ R\) denote the Gabriel topology corresponding to the hereditary torsion theory cogenerated by \(E_ 0\oplus E_ 1\). The following result giving the description of the topology \(F^ 1_ R\) is proved: Let R be a prime Goldie ring having a family of hereditary Noetherian partial quotient rings \(R_{\lambda}\), \(\lambda\in \Lambda\) such that \(R=\cap_{\lambda \in \Lambda}R_{\lambda}\), then \(F^ 1_ R=\{I:\) I is a left ideal in R, \(I^*=R\}\), where \(I^*=Hom(I,R)\). The terminology see in \textit{B. Stenström}'s book ''Rings of quotients'' (1975; Zbl 0296.16001).
Mathematics Subject Classification ID: 16W80
Mathematics Subject Classification ID: 16S90
Mathematics Subject Classification ID: 16D50
Mathematics Subject Classification ID: 16P50
zbMATH DE Number: 3955156
zbMATH Keywords: injective envelope
zbMATH Keywords: Gabriel topology
zbMATH Keywords: hereditary torsion theory
zbMATH Keywords: prime Goldie ring
zbMATH Keywords: Noetherian partial quotient rings
author: Ahmad Haghany
reviewed by: Mihail I. Ursul
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 3955156