RD-flatness and RD-injectivity
Résumé
It is proved that a ring R is RD if and only if each R-module is RD-flat (or RD-coflat). It is shown that each RD-coflat module over a commutative ring R is RD-injective if and only if R is a finite product of artinian valuation rings or finite rings. One gives a characterization of commutative rings for which simple, artinian or noetherian modules are RD-flat or RD-injective. It is also proved that a commutative local artinian ring is RD-injective if and if it is quasi-frobenusien.