Example 5

The mapping $(x_i)_{i \in N} \mapsto x_0^2 + x_1^2 + \ldots + x_n^2 + \ldots$ of $A^{(N)}$ into $A$ is a homogeneous polynomial mapping of degree 2. If $A = 2/22$, it coincides with the linear mapping $(x_i)_{i \in I} \mapsto x_0 + x_1 + \ldots + x_n + \ldots$