Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532120140701Quasi-projective covers of right $S$-acts37456482ENMohammadRoueentanDepartment of Mathematics, College of
Science, Shiraz University, Shiraz 71454, Iran.MajidErshadDepartment of Mathematics, College of Science, Shiraz University, Shiraz 71454, Iran.Journal Article20131227In 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. http://cgasa.sbu.ac.ir/article_6482_f25fef016a297f3166ecafec83d649d8.pdf