Lemma 4

Let E be a graded algebra of type $\mathbf{Z}$ and S a set of homogeneous elements $\neq 0$; the set F of elements of E all of whose homogeneous components $x \neq 0$ satisfy relation (36) for all $y \in S$ is a graded subalgebra of E.

It suffices to note that: (1) if $x', x''$ are two homogeneous elements of the same degree $p$, $y$ a homogeneous element of degree $q$ and $x'y = (-1)^{pq}yx'$, $x''y = (-1)^{pq}yx''$, then also $(x' + x'')y = (-1)^{pq}y(x' + x'')$; (2) if $x', x''$ are two homogeneous elements of respective degrees $p', p''$, $y$ a homogeneous element of degree $q$ and $x'y = (-1)^{p'q}yx'$, $x''y = (-1)^{p''q}yx''$, then