On rings with envelopes and covers regarding to C3, D3 and flat modules.

In this paper, by taking the class of all C 3 (or D 3) right R -modules for general envelopes and covers, we characterize a semisimple artinian ring (or a right perfect ring) via D 3 -covers (or D 3 -envelopes) and a right V -ring (or a right noetherian V -ring) via C 3 -covers (or C 3 -envelopes). By using isosimple-projective preenvelope, we obtained that if R is a semiperfect right FGF ring (or left coherent ring), then every isosimple right R -module has a projective cover. Moreover, we also characterize semihereditary serial rings (respectively, hereditary artinian serial rings) in terms of epic flat (respectively, projective) envelopes. [ABSTRACT FROM AUTHOR]