Example 6

Let $A$ be a graded $K$-algebra of type $\mathbf{Z}$; a graded linear $K$-mapping of degree 0, $d : A \to A$, is defined by taking, for $x_n \in A_n (n \in \mathbf{Z})$, $d(x_n) = nx_n$. This mapping is a derivation of $A$, since, for $x_p \in A_p, x_q \in A_q$,