关于分子生成格

On Moleculely Generated Lattices

In 1988, Pro. Wang Guojun proved that every element of completely distributive lattices is a join of molecules, which are unzero join irrducible elements, in paper6]. Otherwise, the lattices that its each element is a join of its molecules are important lattices. We will have discussed these lattices and will have given some its fundamental properties and some sufficiently and essentialy conditions of which a congruence lattice of a lattice is a moleculely generated lattice in this paper.