THE NECESSARY AND SUFFICIENT CONDITIONS OF THE COMPLETE RINGS OF SETS BEING THE IDEAL LATTICES OF SEMILATTICES OR LATTICES
Yuqi Zhang · Neimenggu Shi-da xuebao. Zhexue shehui kexue hanwen ban · 2004
In this paper,The results below are proved:A complete lattice L is a complete ring of sets (LI(F),I(F)) is the lattice of all ideals of F,and F is a distributive join semilattice which is finitely generated by the set of all completely join irreducible elements of L.If a complete lattice L is isomorphic to the ideal lattice of a lattice K,i.e.,I(K)L,then L is a complete ring of sets K is a strong Sober lattice.