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.
"Rings over which every module has a flat \\delta-cover,"
Turkish Journal of Mathematics: Vol. 37:
1, Article 16.
Available at: https://journals.tubitak.gov.tr/math/vol37/iss1/16