It is well-known that translation projective planes are coordinatized by quasifields. More precisely, a projective plane is translation if and only if it has a ternary-ring $R$ which is linear, the addition in $R$ is associative and the multiplication is right-distributive over addition (or left-disributive, if the lines have the equations $y=ax+b$, not $y=xa+b$ as in the right-distributive case).
Question. Is there any reasonable algebraic characterization of ternary rings of dual translation projective planes (i.e., projective planes which are dual to translation projective planes)?
