Corollary 1

*Let $E'$ be a submodule of a right $A$-module $E$, $F'$ a submodule of a left $A$-module $F$ and $\operatorname{Im}(E' \otimes_A F)$ and $\operatorname{Im}(E \otimes_A F')$ the sub-$\mathbf{Z}$-modules of $E \otimes_A F$, the respective images of the canonical mappings $E' \otimes_A F \to E \otimes_A F$,

Then there is a canonical $\mathbf{Z}$-module isomorphism*

*such that, for $\xi \in E/E'$, $\eta \in F$, $\pi(\xi \otimes \eta)$ is the class of all elements $x \otimes y \in E \otimes_A F$ such that $x \in \xi$ and $y \in \eta$.

Note that when $E$ is a $((B'_i); A, (C'_j))$-multimodule, $F$ a $(A, (B''_h); (C''_k))$-multimodule and $E'$ and $F'$ submultimodules of $E$ and $F$ respectively, the isomorphism (20) is an isomorphism for the $((B'_i), (B''_h); (C'_j), (C''_k))$-multimodule structures of the two sides (no. 3).