I would like to prove that the following conditions for a ring $R$ are equivalent:
1) $R$ is Noetherian and self-injective 2) the class of projective $R$ modules is equal to the class of injective $R$-modules.
I proved 2 implies 1, but I'm having some troubles in proving 1 implies 2, in particular in showing that an injective modules is projective. Any help?
