On the completion by cuts of distributive lattices
Nenosuke Funayama · Proceedings of the Japan Academy Series A Mathematical Sciences · 1944
Is the completion by cuts of modular lattices modular ?Is that of distributive lattices necessarily distributive?This problem was presented by H. Macneille ).G. Birkhoff has listed this problem in his book among unsolved problemsz).In 2 we will solve this pPoblem negatively by constructing an example of a distributive lattice, whose completion by cuts is not modular.In 3 we will give a necessary and sufficient condition for the distributivity of the lattice completed by cuts of a distributive lattice.