Direct product decomposition of molecular lattices and structure of generalized order homomorphisms (Q1823963)

The authors investigate the direct product decomposition of molecular lattices and the structure of generalized order homomorphisms. Main results: 1. Let L be a molecular lattice, \(\{L_ i:\) \(i\in I\}\) be the family of principal sublattices of L, then \(\{L_ i:\) \(i\in I\}\) is a direct product decomposition of L. 2. For any molecular lattice, an irreducible direct product decomposition exists; any two of them are equivalent. 3. Let L, \(L'\) be molecular lattices, \(\{L_ i:\) \(i\in I\}\) be the family of principal sublattices of L. If for each \(i\in I\) a generalized order homomorphism \(f_ i: L_ i\to L'\) is given, then there exists a unique generalized order homomorphism f: \(L\to L'\) such that \(f_ i=f/L_ i\) for each \(i\in I\).