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Defined by Joyce and Matveev, the fundamental quandle is a complete invariantof oriented classical knots. We consider invariants of knots defined fromquotients of the fundamental quandle. In particular, we introduce thefundamental Latin Alexander quandle of a knot and consider its Gr\"obnerbasis-valued invariants, which generalize the Alexander polynomial. We show viaexample that the invariant is not determined by the generalized Alexanderpolynomial for virtual knots.

Quotient Quandles and the Fundamental Latin Alexander Quandle