Definition:Zero Divisor/Warning

Zero Divisor: Warning

Beware the terminology divisor of zero.

It is easy to confuse this with the fact that, for every element $a$ of a ring $R$, from Ring Product with Zero we have that $a \circ 0_R = 0_R$.

Hence one may say that every such element is a divisor of zero.

However, the concept of a zero divisor specifically requires that the $b$ in $a \circ b = 0_R$ is not zero.