Stone algebra

In mathematics, a Stone algebra or Stone lattice is a pseudocomplemented distributive lattice L in which any of the following equivalent statements hold for all

;
;
.

They were introduced by, and named after Marshall Harvey Stone.
The set is called the skeleton of L. Then L is a Stone algebra if and only if its skeleton S is a sublattice of L.
Boolean algebras are Stone algebras, and Stone algebras are Ockham algebras.

Examples

The open-set lattice of an extremally disconnected space is a Stone algebra.
The lattice of positive divisors of a given positive integer is a Stone lattice.