Differentially trivial left Noetherian rings
We characterize left Noetherian rings which have only trivial derivations.
We characterize left Noetherian rings which have only trivial derivations.
Let S = Σi=1n Rai be a finite normalizing extension of R and suppose that SM is a left S-module. Denote by crk(A) the dual Goldie dimension of the module A. We show that crk(RM) ≤ n · crk(SM) if either SM is artinian or the group homomorphism M → aiM given by x → aix is an isomorphism.