Rings over which every module has a flat $delta$-cover

Let M be a module. A $delta$-cover of M is an epimorphism from a module F onto M with a $delta$-small kernel. A $delta$-cover is said to be a flat $delta$-cover in case F is a flat module. In the present paper, we investigate some properties of (flat) $delta$-covers and flat modules having a projective $delta$-cover. Moreover, we study rings over which every module has a flat $delta$-cover and call them right generalized $delta$-perfect rings. We also give some characterizations of $delta$-semiperfect and $delta$-perfect rings in terms of locally (finitely, quasi-, direct-) projective $delta$-covers and flat $delta$-covers.

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