Localization in finite dimensional FPF rings
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.
faithful finitely generated right R-module
scientific article; zbMATH DE number 4075304