Let $R$ be a ring. Then $R$ is also an algebra over the ring of integers if we define the action of $\mathbb{Z}$ on $R$ by the following rules: $$ 0 \cdot x = $$ $$ (n + 1) \cdot x = n \cdot x + $$ $$ (-n) \cdot x = -(n \cdot x $$ In other words, the action of a positive integer $n$ on $x$ is to add $x$ to itself $n$ times and the action of a negative integer $n$ on $x$ is to subtract $x$ to itself $n$ times.