Sufficient conditions for the modularity of the lattice generated by elements with properties of modular type.
It is long known (Grätzer-Schmidt) that in every lattice the sublattice generated by three elements, two of which are standard, is distributive. In the same spirit the paper under review exhibits conditions on three elements of any lattice that guarantee the modularity of the generated sublattice \(S\). Specifically, all combinations of left-modularity, right-modularity, and dual right-modularity that suffice for the modularity of \(S\) are classified. The free modular lattice on three generators is invoked for this purpose.
scientific article; zbMATH DE number 6501742