Corollary

Under the same hypotheses as in Proposition 11, for the endomorphism $\bigwedge(u)$ of the A-module $\bigwedge(M)$

It suffices to replace $\xi$ and $\eta$ by 1 in (18) and observe that the matrix of $\bigwedge(u)$ with respect to the basis of the $e_H$ ($H \in \mathfrak{F}(I)$) is the diagonal matrix of the matrices of the $\bigwedge^k(u)$ for $\geq k$ 0 (II, $§ 10$, no. 7, Example IV).