Superdivisors in Complete Lattices
YU Bu-lei · Journal of Sichuan Normal University · 2010
In this paper,the concept of superdivisor elements is introduced and some properties of superdivisors in complete lattices are shown.Some equivalent conditions for a superdivisor element to be a continuous join-irreducible element are proved.In the end,the structure of complemented modular lattices is described,and a necessary and sufficient condition for a lattice to be a Boole lattice is given,that is,a complete lattice L is a Boole lattice if and only if L is a lower continuous,distributive lattice,and every nonzero elements have only zero superdivisor.