Stone Paradistributive Latticoids (European Journal of Pure and Applied Mathematics, 2025)
We introduce the concept of Stone paradistributive latticoids (Stone PDLs) as a natural generalization of Stone lattices to the broader setting of paradistributive latticoids endowed with parapseudo-complementation. We provide multiple equivalent characterizations of Stone PDLs, both algebraic and topological, including those based on the structure of principal filters, the co-maximality condition of distinct minimal prime filters, and the retract properties of the associated spectral spaces. Moreover, we establish canonical correspondences between prime filters of PDLs and those of associated Boolean algebras, revealing new representation theorems and duality principles. These results unify and extend classical lattice-theoretic frameworks—particularly those concerning Stone lattices—into a more general algebraic logic context, laying a robust foundation for future applications in lattice theory, universal algebra, and topological duality.
Keywords: Paradistributive latticoid; Stone lattice; parapseudo-complementation; prime filter; minimal prime filter