G-filters and Generalized Complemented Distributive Lattices

Authors

  • Jogarao Gunda Department of BS & H, Aditya Institute of Technology and Management, Tekkali, Srikakulam, Andhra Pradesh-530021, India
  • Ramesh Sirisetti Department of Mathematics, GITAM School of Science, GITAM (Deemed to be University), Visakhapatnam, Andhra Pradesh-530045, India
  • Ravikumar Bandaru Department of Mathematics, School of Advanced Sciences, VIT-AP University, Andhra Pradesh-522237, India
  • Rahul Shukla Department of Mathematical Sciences and Computing, Walter Sisulu University, Mthatha 5117, South Africa

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i1.5490

Keywords:

Dense elements, Filters, G-filters, Normal G-filters, quasi-complemented  distributive lattices, generalized complemented distributive lattices

Abstract

In this work, we derive a class of filters (G-filters, normal G-filters, and co-dense filters) in a distributive lattice (with dense elements). We also verify the various algebraic properties of these filters. It is observed that the set of co-dense filters forms an uninduced distributive lattice, and the set of G-filters forms a Boolean algebra. We characterize quasi-complemented distributive lattices using G-filters and normal G-filters. Using normal G-filters, we demonstrate several necessary and sufficient requirements for a distributive lattice to become quasi-complemented. Also, we introduce generalized complementation on a distributive lattice and characterize it in terms of quasi-complemented distributive lattices.

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Published

2025-01-31

Issue

Vol. 18 No. 1: (January 2025)

Section

Nonlinear Analysis

License

Copyright (c) 2025 Jogarao Gunda, Ramesh Sirisetti, Ravikumar Bandaru, Rahul Shukla

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How to Cite

G-filters and Generalized Complemented Distributive Lattices. (2025). European Journal of Pure and Applied Mathematics, 18(1), 5490. https://doi.org/10.29020/nybg.ejpam.v18i1.5490