Here are two different definitions of torsion element.
Let $M$ be an $R$-module and $m\in M$.
Wikipedia: $m$ is a torsion element iff there exists a nonzero regular element $r$ (i.e. Not a zero divisor) such that $rm=0$.
Dummit&Foote: $m$ is a torsion element iff there exists a nonzero element $r$ such that $rm=0$.
Which one of these is the standard definition?