FP-rings

A ring R is called right FP-injective if every R-homomorphism from a finite ly generated submodule of a free right R-module F into R extends to F. In t his paper a ring R will be called a right FP-ring if R is semiperfect, righ t FP-injective and has an essential right socle. The class of FP-rings stri ctly contains the class of right (and left) pseudo-Frobenius rings, and we show that it is right-left symmetric and Morita-invariant. As an applicatio n we show that if R is a left perfect right FP-injective ring, then R is qu asi-Frobenius if and only if the second right socle of R is finitely genera ted as a right ideal of R. This extends the known results in the right self injective case.