Remark

We keep the assumptions and notation above and suppose that the $(B,A)_k$-bimodule Q is the dual $P^*$ of the A-module P and that the isomorphisms $\lambda$ and $\theta$ are the canonical mappings $\Lambda : P\otimes_BP^*\rightarrow_sA_d$ and Θ : $P^*\otimes_AP\rightarrow_sB_d$ (VIII, p. 101, Theorem 1). Since the A-module P is projective and finitely generated, we have a canonical isomorphism $\vartheta_M: P^*\otimes_AM\rightarrow$ Hom$_A(P,M)$ for every A-module M (II, §4, No. 2, p. 271, Corollary). We leave it to the reader to reformulate the results of Subsections 3 and 4 by replacing the construction $M\mapsto Q\otimes_AM$ with the construction $M\mapsto$ Hom$_A(P,M)$.