A ring R is called a right WPF-ring (weak PF-ring) if R is a serniperfect right simple-injective ring with essential right socle. The class of right WPF-rings is broader than that of right PF-rings. In this article, we study and provide several characterizations of this new class of rings. We also show that if R is a left perfect, left and right f-injective ring, then R is QF if and only if Soc(2)(R) is a finitely generated right R-module if and only if R/Soc(R) is a finitely cogenerated left R-module. Some known results are obtained as corollaries. [References: 27]
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