Mohammad Roueentan - Department of Mathematics, College of Science, Shiraz University, Shiraz ۷۱۴۵۴, Iran.
Majid Ershad - Department of Mathematics, College of Science, Shiraz University, Shiraz ۷۱۴۵۴, Iran.

In this paper S is a monoid with a left zero and A_S (or A) is a unitary right S-act. It is shown that a monoid S is right perfect (semiperfect) if and only if every (finitely generated) strongly flat right S-act is quasi-projective. Also it is shown that if every right S-act has a unique zero element, then the existence of a quasi-projective cover for each right act implies that every right act has a projective cover. ‎  

Projective, quasi-projective, perfect, semiperfect, cover