Characteristic
We define the characteristic of a ring \(R\) to be the smallest such positive integer \(m \in \Z^+\) for which:
\[ m \cdot 1=0 \]in \(R\). We denote the characteristic of \(R\) by: \(\text{char}{R}=m\).
(sidenote: When \(R\) is an integral domain , then the characteristic of \(R\) must be a [prime integer](). )