Weakly prime elements in multiplicative lattices

Abstract

In this article, we study weakly prime elements and almost prime elements in multiplicative lattices. Next we characterize weak pi-lattices and weak principal element lattices. We also establish new characterizations for pi-domains and principal element lattices in terms of almost prime elements. Finally, we show that in a Noether lattice L, every proper element of L is a finite product of almost prime elements if and only if L is a finite direct product of principal element domains, special principal element lattices, and special product of almost prime elements lattices.