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Parapseudo-complementation on Paradistributive Latticoidsopen access
- Issue Date
- Apr-2024
- Publisher
- New York Business Global
- Keywords
- Boolean algebra; Filter; Minimal element; Paradistributive Latticoid(PDL); Parapseudo-complementation
- Citation
- European Journal of Pure and Applied Mathematics, v.17, no.2, pp 1129 - 1145
- Pages
- 17
- Indexed
- SCOPUS
ESCI
- Journal Title
- European Journal of Pure and Applied Mathematics
- Volume
- 17
- Number
- 2
- Start Page
- 1129
- End Page
- 1145
- ISSN
- 1307-5543
- 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. © 2024 EJPAM All rights reserved.
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