Dual automorphism-invariant modules over perfect rings

Under study are the dual automorphism-invariant modules and pseudoprojective modules. Some conditions were found under which the dual automorphism-invariant module over a perfect ring is quasiprojective. We also show that if $R$ is a right perfect ring then a pseudoprojective right $R$-module $M$ is finitely generated if and only if $M$ is a Hopf module.