$FP$-injective and weakly quasi-Frobenius rings

The classes of $FP$-injective and weakly quasi-Frobenius rings are investigated. The properties for both classes of rings are closely linked with embedding of finitely presented modules in $fp$-flat and free modules respectively. Using these properties, we characterize the classes of coherent CF- and FGF-rings. Moreover, it is proved that the group ring $RG$ is $FP$-injective (weakly quasi-Frobenius) if and only if the ring $R$ is $FP$-injective (weakly quasi-Frobenius) and $G$ is locally finite.