A commenter on Reddit pointed out that quasigroups require both left and right division operators \ and /, and that even though they are not associative, the ax

A commenter on Reddit pointed out that quasigroups require both left and right division operators \ and /, and that even though they are not associative, the axioms x \ (x * y) = y x * (x \ y) = y (x * y) / y = x (x / y) * y = x must hold -- so in fact, quasigroups are good enough!