ℕ-graded ring

Let \(R\) be a ring. Then \(R\) is said to be graded, if there exists a decomposition

\begin{align*} S = \bigoplus_{n \in \mathbb{N}_0} S_n \end{align*}

such that for \(n,m \in \mathbb{N}_0\) it holds, that

\begin{align*} S_n \cdot S_d = S_{n + d} \end{align*}