polynomial ring as graded ring

Let \(R\) be a ring and \(R[X_i \vert i \in I]\) the polynomial ring. Then \(R[X_i]\) is a graded ring with

\begin{align*} R[X_i] \coloneqq \bigoplus_{n \in \mathbb{N}} R_n \end{align*}

with

\begin{align*} R_n \coloneqq \{f \in R[X_i] \vert \mathrm{deg}(f) = n, f \text{ homogenous}\} \sqcup \{0\} \end{align*}

see: homogeneous polynomial

Let $f =