On copure flat modules and flat resolvents

We prove that (a) if R is left coherent, then a finitely presented right R–module M is copure flat if and only if M is a cokernel of a flat preen-velope (b) if R is a ring and n a nonnegative integer, then r.IFD(R) ≤ n if and only if every nth yoke of each left R–module is copure flat; (c) let R be left and right coherentFP– idRR ≤ 1, n a positive integer and M a finitely presented right R–module, then M is an nth F–cosysygy of a finitely presented right R–module if and only if every finitely generated projective resolution of M is a flat resolvent of the nth syzygy; (d) if R is left coherent and n a nonnegative integer, then FP – idfRR ≤ n if and only if every projective resolution of the nth syzygy of each finitely presented left R–module is a flat resolvent.