Definition:Characteristic of Ring/Definition 1

Definition
Let $\struct {R, +, \circ}$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.

Let $n \cdot x$ be defined as in Definition:Power of Element.

The characteristic $\Char R$ of $R$ is the smallest $n \in \Z, n > 0$ such that $n \cdot 1_R = 0_R$.

If there is no such $n$, then $\Char R = 0$.

Also see

 * Equivalence of Definitions of Characteristic of Ring