WEAKLY PRIME ELEMENTS IN MULTIPLICATIVE LATTICES

Callialp F., Jayaram C., TEKİR Ü.

COMMUNICATIONS IN ALGEBRA, vol.40, no.8, pp.2825-2840, 2012 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 40 Issue: 8
  • Publication Date: 2012
  • Doi Number: 10.1080/00927872.2011.587212
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.2825-2840
  • Keywords: Almost prime element, Invertible element, pi-Lattice, Principal element, Principal element lattice, Regular lattice, Weak pi-lattice, Weakly prime element, Weak principal element lattice
  • Marmara University Affiliated: Yes

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.