Let $R$ be a nonzero commutative ring. For each $c \in R$, define the multiplication map
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\begin{align*}
m_c: R &\to R
\end{align*}
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by $m_c(x)=cx$ for every $x \in R$. Then $R$ is an [integral domain](/page/Integral%20Domain) if and only if, for every $c \in R$ with $c \ne 0_R$, the map $m_c$ is injective.