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 $\Lambda/(\Delta_{ L}(t))$.
Categories: math.GT