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. It is here: http://en.wikipedia.org/wiki/Nakayama%27s_conjecture Thanks.
The following remark can be found in Morita Contexts, Idempotents, and Hochschild Cohomology — with Applications to Invariant Rings by Ragnar-Olaf Buchweitz (arXiv):
Here, SNC denotes the strong Nakayama conjecture and GNC the generalized Nakayama conjecture. For their meaning, see loc. cit.