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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?

2 Answers 2