\begin{definition}[Definition:Characteristic of Ring/Definition 3]
Let $\struct {R, +, \circ}$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.
The '''characteristic of $R$''', denoted $\Char R$, is defined as follows.
Let $p$ be the order of $1_R$ in the additive group $\struct {R, +}$ of $\struct {R, +, \circ}$.
If $p \in \Z_{>0}$, then $\Char R := p$.
If $1_R$ is of infinite order, then $\Char R := 0$.
\end{definition}