On rings whose finitely generated faithful modules are generators (Q1121357)

This paper addresses a number of open questions about FPF rings, i.e., rings all of whose finitely generated faithful modules are generators. For instance, examples are constructed to show that: (1) semiprime FPF rings need not be semihereditary; (2) Pierce stalks of semiprime FPF rings need not be FPF; (3) centers of semiprime FPF rings need not be FPF; (4) Galois subrings of semiprime FPF rings need not be FPF. Among the positive results obtained are: (5) Galois subrings of commutative semiprime FPF rings are FPF; (6) over a commutative FPF ring, the group ring of any finite group whose order is invertible is FPF.