Direct and Subdirect Factorizations of Lattices
Fumitomo Maeda · Hiroshima Mathematical Journal · 1951
Let a lattice L be a product 0 L 1 ••• Ln of n lattices Li (i=l, ... , n).If L has the null element O and the unit element 1, then Lt has the null element Oi and the unit element 1..The element z, which is expressed inThe center of L is a Boolean algebra, and using this center we can easily solve the factorization problem of lattices 3 ).But for the lattices L without O or 1, the centers of L do not exist.Hence for the factorization problem of such lattices, we must seek Boolean algebras.From this point of view, I investigated the direct factorizations and the subdirect factorizations of lattices without the assumption that O and 1 exist.