$\mathcal{l}$-prime elements in multiplicatice lattices

Abstract.

In this paper we study $\mathcal{l}$-prime elements in C-lattices and characterize Prüfer lattices, almost principal element lattices and principal element lattices in terms of $\mathcal{l}$-prime elements. Using these results, some new characterizations are given for general ZPI-rings and almost multiplication rings. Finally some new equivalent conditions are given for Dedekind lattices.