Comparing the bounded derived categories of an algebra and of the endomorphism algebra of a given support -tilting module, we find a relation between the derived dimensions of an algebra and of the endomorphism algebra of a given -tilting module.
We show here that a directing component of the Auslander-Reiten quiver of a quasitilted algebra is either postprojective or preinjective or a connecting component.
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.