Characteristic of a ring

From Commalg
Jump to: navigation, search


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