Parapseudo-complementation on Paradistributive Latticoids

Authors

  • Suryavardhani Ajjarapu Department of Mathematics, GITAM Deemed to be University,\\ Hyderabad Campus, Telangana-502329, 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
  • Young Bae Jun Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

DOI:

https://doi.org/10.29020/nybg.ejpam.v17i2.5042

Keywords:

Parapseudo-complementation, Paradistributive Latticoid, Minimal element, Filter, Boolean algebra

Abstract

In this paper, we introduce the concept of a parapseudo-complementation in a paradistributive latticoid(PDL) and investigate its elementary properties. We demonstrate the independence of the axioms related to its definition, highlighting the flexibility of this concept. Additionally, we establish necessary conditions for a PDL with a minimal element to be parapseudo-complemented and explore the properties required for parapseudo-complementation to be equationally definable. Moreover, we establish a one-to one correspondence between the set of all minimal elements and the set of all parapseudo-complementations.

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Published

2024-04-30

Issue

Vol. 17 No. 2: (April 2024)

Section

Nonlinear Analysis

License

Copyright (c) 2024 European Journal of Pure and Applied Mathematics

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How to Cite

Parapseudo-complementation on Paradistributive Latticoids. (2024). European Journal of Pure and Applied Mathematics, 17(2), 1129-1145. https://doi.org/10.29020/nybg.ejpam.v17i2.5042