TITLE: Is the notation for '$a$ divides $b$' standard?
QUESTION [11 upvotes]: I know that the notation $a | b$ means that there exists an integer $c$ such that $ac=b$, but is this notation completely standard and there's no way that it could be the other way round?

REPLY [8 votes]: In number theory and algebra  $\rm\:a\ |\ b\ $ in ring $\rm\:R\:$ means $\rm\: \exists\: c\in R:\ ac = b,\,$ i.e. $\rm\,ax=b\,$ has at least one solution $\rm\,x\,$ in $\,\rm R.\,$  Usually the ring is omitted, being understood from  ambient context. This notation is used so widely that it surely can be considered standard notation.
Occasionally some authors introduce asymmetric variants, with the bar being tilted, or with "hooks" on the top/bottom of the bar, intended to give some visual cue as to which argument is to be pushed to the bottom of a fraction, or pulled to the top. However, as convenient as they may be, none of these asymmetric variants is in wide use.