In this paper we derive some of the structure of semiperfect FPF rings. A ring is right FPF if every f.g. faithful right module is a generator. For semiperfect right and left FPF rings we show that if all one sided zero divisors are two sided zero divisors, then the classical and maximal quotient rings coincide (all four of them) and are self-injective. We show that if the intersection of the powers of the Jacobson radical is zero, then right and left regular elements are regular. Also, we show

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... right FPF semiperfect rings contain the singular submodule of their injective hulls and that every finitely generated module contained in the injective hull and containing the ring is isomorphic to the ring.