  In this paper, we study the colorability of link diagrams by the Alexander
quandles. We show that if the reduced Alexander polynomial $\Delta_{L}(t)$ is
vanishing, then $L$ admits a non-trivial coloring by any non-trivial Alexander
quandle $Q$, and that if $\Delta_{L}(t)=1$, then $L$ admits only the trivial
coloring by any Alexander quandle $Q$, also show that if $\Delta_{L}(t)\not=0,
1$, then $L$ admits a non-trivial coloring by the Alexander quandle
$\Lambda/(\Delta_{L}(t))$.
