No abstract

In this paper, by taking the class of all [Formula: see text] (or [Formula: see text]) right [Formula: see text]-modules for general envelopes and covers, we characterize a semisimple artinian ring (or a right perfect ring) via [Formula: see text]-covers (or [Formula: see text]-envelopes) and a right [Formula: see text]-ring (or a right noetherian [Formula: see text]-ring) via [Formula: see text]-covers (or [Formula: see text]-envelopes). By using isosimple-projective preenvelope, we obtained that if [Formula: see text] is a semiperfect right FGF ring (or left coherent ring), then every isosimple right [Formula: see text]-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.

In this paper, we investigate semiperfect rings over which every finitely generated right module is a direct sum of a projective module and a singular module. As applications, we obtain several characterizations of right co-Harada rings.

No abstract