  We show that the Auslander-Reiten conjecture on stable equivalences holds
true for principal centralizer matrix algebras over an arbitrary field and for
Frobenius-finite algebras over an algebraically closed field, that stable
equivalences of algebras with positive $\nu$-dominant dimensions preserve
stable equivalences of their Frobenius parts, and that the delooping levels,
$\phi$-dimensions and $\psi$-dimensions are invariants of stable equivalences
of Artin algebras without nodes.
