  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.
