  We introduce and study the notion of pseudo-Frobenius graded algebra with
enough idempotents, showing that it follows the pattern of the classical
concept of pseudo-Frobenius (PF) and Quasi-Frobenius (QF) rings, in particular
finite dimensional self-injective algebras, as studied by Nakayama, Morita,
Faith, Tachikawa, etc. We show that such an algebra is characterized by the
existence of a graded Nakayama form. Moreover, we prove that the
pseudo-Frobenius property is preserved and reflected by covering functors, a
fact that makes the concept useful in Representation Theory.
