CHARACTIZATION THEOREMS FOR A COMPLETELY DISTRIBUTIVE LATTICE BEING A COMPLETE RING OF SETS
Yuqi Zhang · Neimenggu Shi-da xuebao. Zhexue shehui kexue hanwen ban · 2002
By using the subdirect product representation theorem for completely distributive lattices of Raney G N,the following results are proved.A completely distributive lattice L is a complete ring of sets??L is a relatively atomic lattice.A completely distributive lattice L is a complete ring of sets??con c(L) is isomorphic to a power set lattice,where con c(L) is the lattice of all complete congruences of L.