Semi-perfect FPF rings and applications
A ring R is right FPF if every finitely-generated faithful right R-module is a generator. Let R be a semi-perfect right FPF ring in which right regular elements are regular. It is shown that R has a semi-perfect right self-injective left and right classical quotient ring. Also R is a direct product of matrix rings over serial domains and a ring whose right singular ideal is essential as a right ideal. This is used to give information about when R has a QF quotient ring and about the case in which R is right or left Noetherian. The hypothesis that right regular elements of R are regular is added to the statements of several of the results in a note at the end of the paper.
scientific article; zbMATH DE number 4002313
scientific article