$χ$ -extending modular lattices
Jesus Adrian Celis-González, Hugo Alberto Rincón-Mejía
Published: 2025/9/26
Abstract
This paper investigates the theory of lattices, focusing on extending lattices relative to abstract classes, modular lattices, and torsion lattices. Definitions of type-1 and type-2 extending lattices are provided, along with their weakly extending counterparts. Modular and upper continuous lattices are analyzed, with lemmas establishing relationships between pseudo-complements, complements, and essential elements. Applications to module theory are highlighted.