If R is a ring without zero
divisors then it is shown that any torsion-free quasi-projective left R-module A is
projective provided A is finitely generated or A is “big”. It is proved that the
universal existence of quasi-projective covers in an abelian category with enough
projectives always implies that of the projective covers. Quasi-projective modules
over Dedekind domains are described and as a biproduct we obtain an infinite family
of quasi-projective modules Q such that no direct sum of infinite number of
carbon copies of Q is quasi projective. Perfect rings are characterised by
means of quasi-projectives. Finally the notion of weak quasi-projectives is
introduced and weak quasi-projective modules over a Dedekind domain are
investigated.
