Abstract
In generalizing the well-established notion of projective cover, the notions of D3-cover and rad-projective cover were recently introduced and new characterizations of perfect and semiperfect rings were provided. On the other hand, Y. Zhou introduced and studied the notions of delta-cover, delta-perfect and delta-semiperfect rings. In this paper we combine and generalize these notions and introduce the new notions of rad-projective delta-cover and D3-delta-cover. New characterizations of delta-perfect and delta-semiperfect rings are provided.