Characteristic of a ring

Definition

Let $R$ be a ring. The characteristic of a ring is defined as follows:

• If $\exists n\in\mathbb{N}_{\ge 0}$ such that $\forall a\in R$ we have $na=0$ then the smallest such integer $n$ is the characteristic of $R$
• If $\nexists$ such an $n$ we say $R$ has characteristic 0