Neutrosophic 2-absorbing primary ideals on lattices

Abstract Recent advances in neutrosophic lattice theory have highlighted its potential to model uncertainty, indeterminacy, and inconsistency more effectively than classical and intuitionistic fuzzy approaches. Building upon foundational studies that introduced neutrosophic lattices and their extensions through soft structures, concept lattices, triangular norms, and lattice-valued neutrosophic sets, this study contributes to the growing body of research on neutrosophic ideals. We introduce and investigate several key notions in the context of lattices, including neutrosophic prime ideals, prime neutrosophic ideals, neutrosophic 2-absorbing ideals, 2-absorbing neutrosophic ideals, neutrosophic primary ideals, and primary neutrosophic ideals. A special focus is placed on the characterization of neutrosophic 2-absorbing primary ideals, accompanied by an analysis of the transitions among these concepts and their interrelationships with traditional lattice ideals. Furthermore, these structures are examined within lattices formed by Cartesian products, offering new perspectives on their behavior in complex settings.