Weakly Prime Elements in Multiplicative Lattices

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In this article, we study weakly prime elements and almost prime elements in multiplicative lattices. Next we characterize weak π-lattices and weak principal element lattices. We also establish new characterizations for π-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.