Example 2

Let $(N_i)_{i \in I}$ be a family of A-modules, $f_i$ a mapping of M into $N_i, i \in I$, and $f : M \to \prod_{i \in I} N_i$ the mapping with components $f_i$. For f to be a homogeneous polynomial mapping of degree q it is necessary and sufficient that each $f_i$ be a homogeneous polynomial mapping of degree q.