D-Pseudo Supplemented Almost Distributive Lattices
Asia Pacific Journal of Mathematics · 2024
In this paper, we introduce D-pseudo supplementation and it's dual on (almost distributive lattices) ADLs (with dense elements) which is a generalization of pseudo supplemented ADLs, we obtain some algebraic properties and characterize both using the set BD(A) = {a1 ∈ L | there exists a2 ∈ L such that a1 ∧ a2 = 0 and a1 ∨ a2 is desne}, where A is an ADL with dense elements.Finally, we prove a one to one correspondence between D-pseudo supplemented ADLs (dual D-pseudo supplemented ADLs) and the class of principal ideals (sectionally intervals) in an ADL.