Let be a binary operation, i.e. is a magma. We say that the operation is
- left self-distributive if for all , ;
- right self-distributive if for all , .
The binary operation in any semilattice is self-distributive on both sides, following from associativity, commutativity, and idempotence.
The operations in a rack (and hence also in a quandle) are self-distributive on the side on which they act. In particular, this includes the operation of conjugation in a group.
A Laver table? is the multiplication table of a self-distributive operation.
Revised on September 9, 2011 01:12:59
by Mike Shulman