${\bullet}$-Paradistributive Latticoids
Ravikumar Bandaru, Suryavardhani Ajjarapu, Noorbhasha Rafi, Rahul Shukla · European Journal of Pure and Applied Mathematics · 2025
In this paper, we introduce the notion of a new class of Paradistributive latticoids termed ${\bullet}$-PDLs and investigate its properties. In addition, we prove that a Paradistributive latticoid(PDL) $\LomV$ is a ${\bullet}$-PDL iff $\LomV/\theta$ is a Boolean algebra with a minimal element, where $\theta =\{(\x,\y) \in \LomV \times \LomV \mid [\x]^{\bullet}=[\y]^{\bullet}\}$ is a congruence relation on $\LomV$. Further, we explore the concept of dense elements in a PDL and characterize $\bullet$-PDL in terms of dense elements. Also, we introduce the notion of a disjunctive PDL and we give equivalent conditions for a $\bullet$-PDL to be a disjunctive PDL.