Closed Ideals and Annihilators of Distributive Dual Weakly Complemented Lattice

Abstract

The goal of this paper is study closed ideals and annihilators over the class of distributive dual weakly complemented lattices(DDWCL's). The algebraic structure of ideals, closed ideals and dense ideals are shown. The connection between closed ideals andannihilators in this class is obtained.

Orthopseudorings and congruences on distributive lattice with dual weak complementation

“…The skeleton of is an ortho-lattice under operations: for all . Also, is an ortho-complement of I , refer to [8] .…”

Annihilator Hyperideals in Strong Bounded Dual Distributive Meet-hyperlattice

“…As a generalization of lattices Halaš [6] studied annihilators in ordered sets. This was followed by a lot of studies and research on the concept of annihilator in many algebraic structures and classes, for instance: almost distributive lattices [3],0-almost distributive lattices [4], distributive dual weakly complemented lattice [17], BCK-algebras [7], standard QBCC algebras [14], C-algebra [16], and many other classes.…”