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)

License

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

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Upon acceptance of an article by the journal, the author(s) accept(s) the transfer of copyright of the article to European Journal of Pure and Applied Mathematics.

European Journal of Pure and Applied Mathematics will be Copyright Holder.

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