Characteristic of a ring

Definition

Let $R$ be a commutative unital ring. Consider the natural homomorphism from $\mathbb {Z}$ to $R$ that sends $1\in \mathbb {Z}$ 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