Weakly prime elements in multiplicative lattices
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CitationÇALLIALP, F., JAYARAM, C., TEKİR, Ü. (2012). Weakly prime elements in multiplicative lattices. Communications in Algebra, 40(8), pp. 2825-2840. http://dx.doi.org/10.1080/00927872.2011.587212.
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.
SourceCommunications in Algebra
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