${\bullet}$-Paradistributive Latticoids

Authors

  • Ravikumar Bandaru Department of Mathematics, School of Advanced Sciences, VIT-AP University, Amaravati-522237, Andhra Pradesh, India
  • Suryavardhani Ajjarapu Department of Mathematics, GITAM Deemed to be University, Hyderabad Campus, Telangana-502329, India
  • Noorbhasha Rafi Department of Mathematics, Bapatla Engineering College, Bapatla, Andhra Pradesh, India-522 102
  • Rahul Shukla Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha 5117, South Africa

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i2.5705

Keywords:

${\bullet}$-PDL, Congruence relation, Boolean algebra, Dense element, Disjunctive PDL

Abstract

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.

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Published

2025-05-01

Issue

Vol. 18 No. 2: (April 2025)

Section

Algebra

License

Copyright (c) 2025 Ravikumar Bandaru, Suryavardhani Ajjarapu, Noorbhasha Rafi, Rahul Shukla

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How to Cite

${\bullet}$-Paradistributive Latticoids. (2025). European Journal of Pure and Applied Mathematics, 18(2), 5705. https://doi.org/10.29020/nybg.ejpam.v18i2.5705