Coloring link diagrams by Alexander quandles

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