Note on the Sublattice Generated by Two Finite Sequences in a Modular Lattice
Min Youlin (Jiangxi Education Collage)
With a new method, more briefly than 69 we prove. THEOREM 1 A lattice L is a modular lattice iff the sublattice L_1~ generated by arbitrary two sequences a=c_0c_1~…c_m=b a=d_0d_1~…d_n=b in L is a distributive lattice. We also obtain THEOREM 2 If Twain ring ∑ is normal,then the lattice Q of δ-congruence of ∑ is a distributive lattice.