Definition:Characteristic of Ring/Definition 1

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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


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