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.

The following remark can be found in Morita Contexts, Idempotents, and Hochschild Cohomology
— with Applications to Invariant Rings by Ragnar-Olaf Buchweitz (arXiv):

Remarks 3.2. (1) The conjectures (INC’), (INC) trivially hold if the algebras
  C,B involved are already commutative noetherian rings. However, there seems to
  be no real advantage gained in either (SNC) or (GNC) if one assumes that A is
  already commutative. In this sense, the aforementioned conjectures truly belong to
  the realm of (slightly) noncommutative algebra.

Here, SNC denotes the strong Nakayama conjecture and GNC the generalized Nakayama conjecture. For their meaning, see loc. cit.
