Suppose $x,y \in R$ where $R$ is a ring (not necessarily with an identity) and suppose $m$ is a positive integer. What is the characteristic of a ring with the property that if $mx = my$, then $x = y$?
This is not true if the characteristic divides $m$.
If the characteristic has a factor in common with $m$, then in some rings of integers modulo $n$ this would not be true either for every $x,y$.
So is it only true in characteristic 0 rings?