Proposition 6 (*« Euler's identity »*)

— Let $u \in \mathbf{A}[\mathbf{X}]$ be a homogeneous polynomial of degree r ; we have

Let D be the A-linear mapping of $A[X]$ into itself such that $D(v) = sv$ when v is homogeneous of degree s. We know (III, p. 554, Example 6) that D is a derivation of $A[X]$. Thus Prop. 6 is a Corollary of Prop. 4 (IV, p. 6).