Abstract
In this paper, we study the colorability of link diagrams by the Alexander quandles. We show that if the reduced Alexander polynomial ΔL(t) is vanishing, then L admits a non-trivial coloring by any non-trivial Alexander quandle Q, and that if ΔL(t) = 1, then L admits only the trivial coloring by any Alexander quandle Q, also show that if ΔL(t) ≠ 0, 1, then L admits a non-trivial coloring by the Alexander quandle Λ/(ΔL(t)).
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