# Characteristic (algebra)

In mathematics, the **characteristic** of a ring *R*, often denoted char(*R*), is defined to be the smallest number of times one must use the ring's multiplicative identity (1) in a sum to get the additive identity (0). If this sum never reaches the additive identity the ring is said to have characteristic zero.

That is, char(*R*) is the smallest positive number *n* such that:[1]^{(p 198, Thm. 23.14)}

if such a number *n* exists, and 0 otherwise.