  Defined by Joyce and Matveev, the fundamental quandle is a complete invariant
of oriented classical knots. We consider invariants of knots defined from
quotients of the fundamental quandle. In particular, we introduce the
fundamental Latin Alexander quandle of a knot and consider its Gr\"obner
basis-valued invariants, which generalize the Alexander polynomial. We show via
example that the invariant is not determined by the generalized Alexander
polynomial for virtual knots.
