Noetherian lattices in which every element is a product of primary elements (Q1908936)

The purpose of this paper is to characterize those Noetherian lattices with the property that every element is a product of primary elements. We show that if an element \(b\) of the lattice \(L\) has a normal decomposition involving only prime elements that are either maximal or multiplication elements, then \(b\) is a product of primary elements (Theorem 2). Our main result is that every element in a Noetherian lattice \(L\) is a product of primary elements if and only if every nonmaximal prime element of \(L\) is a multiplication element (Theorem 4).