Dergiler / Turkish Journal of Mathematics / 2013 / Cilt: 37 - Sayı: 1
Rings over which every module has a flat \d-cover
- Sayfa
- 182–194
- DOI
- —
Özet
Let M be a module. A d-cover of M is an epimorphism from a module F onto M with a d-small kernel. A d-cover is said to be a flat d-cover in case F is a flat module. In the present paper, we investigate some properties of (flat) d-covers and flat modules having a projective d-cover. Moreover, we study rings over which every module has a flat d-cover and call them right generalized d-perfect rings. We also give some characterizations of d-semiperfect and d-perfect rings in terms of locally (finitely, quasi-, direct-) projective d-covers and flat d-covers.
Abstract
Let M be a module. A d-cover of M is an epimorphism from a module F onto M with a d-small kernel. A d-cover is said to be a flat d-cover in case F is a flat module. In the present paper, we investigate some properties of (flat) d-covers and flat modules having a projective d-cover. Moreover, we study rings over which every module has a flat d-cover and call them right generalized d-perfect rings. We also give some characterizations of d-semiperfect and d-perfect rings in terms of locally (finitely, quasi-, direct-) projective d-covers and flat d-covers.