Self-distributive operation

Summary

A self-distributive operation is a binary operation that distributes over itself, on the left or on the right. Left self-distributivity reads $x * (y * z) = (x * y) * (x * z)$. Conjugation in a group, the join and meet of a lattice, and the operation $2x - y$ on an abelian group are self-distributive. Left self-distributive magmas are called shelves; together with racks and quandles they are used in knot theory and in set theory through the Laver tables.