RD-flatness and RD-injectivity

Francois Couchot (1)

1 LMNO - Laboratoire de Mathématiques Nicolas Oresme

It is proved that every commutative ring whose RD-injective modules are $\Sigma$-RD-injective is the product of a pure semi-simple ring and a finite ring. A complete characterization of commutative rings for which each artinian (respectively simple) module is RD-injective, is given. These results can be obtained by using the properties of RD-flat modules and RD-coflat modules which are respectively the RD-relativization of flat modules and fp-injective modules. It is also shown that a commutative ring is perfect if and only if each RD-flat module is RD-projective.

Mots clés: RD-flat module; RD-coflat module; RD-ring; RD-injectivity

Domaines: Anneaux et algèbres [math.RA]

Francois Couchot. RD-flatness and RD-injectivity. Communications in Algebra, 2006, 34, pp.3675--3689. ⟨10.1080/00937870600860817⟩. ⟨hal-00002962v3⟩