Localization in finite dimensional FPF rings
type: Item
instance of: scholarly article
title: Localization in finite dimensional FPF rings
zbMATH Open document ID: 0658.16002
author: Theodore G. Faticoni
published in: Pacific Journal of Mathematics
publication date: 1988-01-01T00:00:00Z
review text: A ring (with 1) is right FPF if each faithful finitely generated right \(R\)-module is a generator of the category mod-\(R\) of right \(R\)-modules. \textit{C. Faith} [Injective modules and injective quotient rings. New York etc.: Marcel Dekker (1982; Zbl 0484.16009)] conjectured that a right and left FPF ring \(R\) has a self-injective classical quotient ring, and proved this when \(R\) is commutative. Further evidence in support of this conjecture is given in [\textit{C. Faith} and \textit{S. S. Page}, FPF ring theory. Cambridge etc.: Cambridge University Press (1984; Zbl 0554.16007)], for example. In this paper a unified approach is given to this and related questions, for the case when \(R\) has finite right Goldie dimension.
Mathematics Subject Classification ID: 16P50
Mathematics Subject Classification ID: 16P60
Mathematics Subject Classification ID: 16E10
Mathematics Subject Classification ID: 16L60
zbMATH DE Number: 4075304
zbMATH Keywords: faithful finitely generated right R-module
zbMATH Keywords: generator
zbMATH Keywords: left FPF ring
zbMATH Keywords: self-injective classical quotient ring
zbMATH Keywords: right Goldie dimension
reviewed by: Kenneth A. Brown
MaRDI profile type: Publication
full work available at URL: pjm.1988.134.79
OpenAlex ID: W2090229602
DOI: 10.2140/PJM.1988.134.79
description: scientific article; zbMATH DE number 4075304