Noetherian algebras of finite self-injective dimension

Let R be a commutative noetherian ring and A a noetherian R-algebra. Take a minimal injective resolution R -> I-center dot and set V-center dot = Hom(R)(center dot) (A, I-center dot). We deal with the case where V-center dot is a dualizing complex for A. We show that A itself is a dualizing complex for A if and only if V-center dot is isomorphic to a tilting complex in D(Mod-A) and that if A is a dualizing complex for A, then - circle times(A)(L) V-center dot induces a self-equivalence of D-b (mod-A).