\begin{definition}[Definition:Characteristic of Ring/Definition 2]
Let $\struct {R, +, \circ}$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.
Let $g: \Z \to R$ be the initial homomorphism, with $\map g n = n \cdot 1_R$.
Let $\ideal p$ be the principal ideal of $\struct {\Z, +, \times}$ generated by $p$.
The '''characteristic''' $\Char R$ of $R$ is the positive integer $p \in \Z_{\ge 0}$ such that $\ideal p$ is the kernel of $g$.
\end{definition}