Nakayama Conjecture. The commutative case. 
Is the Nakayama conjecture solved in the commutative case? It states that "if all the modules of a minimal injective resolution of an Artin algebra $R$ are injective and projective, then $R$ is self-injective". 

I tried to look up but could not find if it is solved or not solved in the commutative case. Can someone provide a reference if it is solved in the commutative case? The Wikipedia page does not say if it is solved in the commutative case. 
Thanks.

A commutative artin algebra is a product of local algebras. The Nakayama conjecture is trivial for local non-selfinjective algebras since the injective envelope of the regular module can not be projective. 
