# Non-separable center of a lattice (Solved)

I will call center of a bounded distributive lattice the sublattice of all complemented elements of .

I will call a bounded distributive lattice a lattice with separable center when

Equivalently a bounded distributive lattice with separable center is such a bounded distributive lattice that

**Conjecture**There exist bounded distributive lattices which are not with separable center.

(Previously this problem was erroneously stated without the word *distributive*, it is corrected now.)

This conjecture follows from William Elliot's post in sci.math and the criterion of a lattice to be distributive, see here.

So the problem solves positively.

Admins: Should I delete this problem from Open Problem Garden because its solution was too easy (found in less than one day). Or just to leave it marked as solved?

## Bibliography

* indicates original appearance(s) of problem.