A note on distributive sublattices of a lattice
Saburo Tamura · Proceedings of the Japan Academy Series A Mathematical Sciences · 1971
In [1], B. J6nsson gave a necessary and sufficient condition for a subset of a modular lattice to generate a. distributive lattice.R. Balbes proved JSnsson's theorem without using Zorn's lemma in [2].In [3],we gave a necessary and sufficient condition that the sublattice gener- ated by a subset H o a lattice should be distributive.In this note we prove this theorem without using Zorn's lemma.And then the condi- tion for the case of H--(x, y, z} is expressed by seven lattice polynomial equations.1o The finite join of elements in H is called a U-element.The