Parapseudo-complementation on Paradistributive Latticoids
Suryavardhani Ajjarapu, Ravikumar Bandaru, Rahul Shukla, Young Bae Jun · European Journal of Pure and Applied Mathematics · 2024
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.