We introduce an algebraic structure we call semiquandles whose axioms are
derived from flat Reidemeister moves. Finite semiquandles have associated
counting invariants and enhanced invariants defined for flat virtual knots and
links. We also introduce singular semiquandles and virtual singular
semiquandles which define invariants of flat singular virtual knots and links.
As an application, we use semiquandle invariants to compare two Vassiliev
invariants.Comment: 14 page