Self-injective noetherian rings

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?

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 sofia-new.nmsu.edu/~elbert/DirectSumRepsOfInjectives.pdf – YACP Dec 4 '12 at 1:37