Remark 2

The notation K, N and $\Gamma$ has the same meaning as before. For each integer $n \geqslant 1$, let $A_n$ be the tensor product of n K-algebras identical with $N$; let $B_n$ be the set of mappings of $\Gamma^{n-1}$ into $N$. By induction on $n$ we can deduce from the Cor. of Prop. 8 the existence of an isomorphism $\varphi_n : A_n \to B_n$, mapping $x_1 \otimes \ldots \otimes x_n$ to the function $(\sigma_1, \ldots, a, ) \quad \sigma_1(x_1) \cdot \sigma_n(x_{n-1})\,x_n$.