Let $R$ be a commutative ring with identity $1_R$ and zero element $0_R$. Let $\mathbb{N}_0 := \mathbb{N} \cup \{0\}$, and let $R[x]$ denote the set of finitely supported functions $a: \mathbb{N}_0 \to R$, written as polynomials $\sum_{i=0}^{m} a_i x^i$, with coefficientwise addition and finite convolution multiplication. For all $p,q \in R[x]$, the sum $p+q$ and product $pq$ belong to $R[x]$. With these operations, $R[x]$ is a commutative ring with identity, whose multiplicative identity is the constant polynomial $1_R$.