Corollary

— Let M be a free A-module, N an A-module, q a positive integer, $h \in \mathbf{Pol}^q(M, N)$ and $(e_i)_i$, a basis of M. In the two cases of Prop. 16 there exists a unique family $(u,$, $\mathbf{N}^{(I)}, |\cdot|$, , of elements of N such that $h \left( \sum_{i \in I} \lambda_i e_i \right) = \sum_{|\nu| = q} \lambda^\nu u_\nu$ for all $(\lambda_i) \in \mathbf{A}^{(1)}$