Corollary

The A-module $\bigwedge^n(M)$ is the image under isomorphism (14) of the submodule of $\bigotimes_{\lambda \in L} \bigwedge(M_\lambda)$* the direct sum of the submodules $\bigwedge^\nu(M)$* for all families $\nu = (n_\lambda) \in \mathbf{N}^{(L)}$* such that $\sum_{\lambda \in L} n_\lambda = n$; if $J$* is the support of* $\nu$, $\bigwedge^\nu(M)$* is canonically isomorphic to $\bigotimes_{\lambda \in J} \bigwedge^{n_\lambda}(M_\lambda)$.

In general $\bigwedge^\nu(M)$, $\bigotimes_{\lambda \in J} \bigwedge^{n_\lambda}(M_\lambda)$ and their image in $\bigwedge^n(M)$ are identified. With this convention: