Characteristic of a ring

Definition
Let $$R$$ be a commutative unital ring. Consider the natural homomorphism from $$\Z$$ to $$R$$ that sends $$1 \in \Z$$ to $$1 \in R$$. The positive element that generates the kernel of this map, is termed the characteristic of $$R$$.

In other words, the characteristic of $$R$$ is the smallest number $$n$$ such that $$1 + 1 + \ldots + 1 = 0$$ when $$1$$ is written $$n$$ times.

Related ring properties

 * Equicharacteristic ring