In this paper, by taking the class of all C3 (or D3) right R-modules for general envelopes and covers, we characterize a semisimple artinian ring (or a right perfect ring) via D3-covers (or D3-envelopes) and a right V-ring (or a right noetherian V-ring) via C3-covers (or C3-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.

中文翻译：

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在带有 C3、D3 和扁平模块的信封和盖子的环上

在本文中，通过取所有类C3（要么D3） 正确的R- 用于一般信封和封面的模块，我们通过D3-封面（或D3-信封）和权利五-ring（或正确的 noetherian五-环）通过C3-封面（或C3-信封）。通过使用等简投影前包络，我们得到如果R是一个半完全右 FGF 环（或左相干环），那么每个等单右R-module 有一个投影覆盖。此外，我们还根据史诗扁平（分别为射影）包络来表征半遗传序列环（分别为遗传性 artinian 序列环）。