A Certain Class of Filters in Generalized Complemented Distributive Lattices

Authors

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

DOI:

https://doi.org/10.29020/nybg.ejpam.v18i1.5535

Keywords:

Filters, Distributive lattices, Ideals

Abstract

In this paper, we introduce $K^g$-filters jointly  derived from the class of ideals and the class of generalized complementations  in a generalized complemented distributive lattice. We obtain some algebraic properties on the obtained class, and we provide some counter-examples. Mainly we derive some Boolean algebras (distributive lattices) through the class of $K^g-$filters in a generalized complemented distributive lattice. Finally, we introduce normal $K^g$-filters in a generalized complemented distributive lattice and then prove that the class of normal $K^g$-filters is a Boolean algebra.

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Published

2025-01-31

Issue

Vol. 18 No. 1: (January 2025)

Section

Nonlinear Analysis

License

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

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How to Cite

A Certain Class of Filters in Generalized Complemented Distributive Lattices. (2025). European Journal of Pure and Applied Mathematics, 18(1), 5535. https://doi.org/10.29020/nybg.ejpam.v18i1.5535