$\chi$ -extending modular lattices
Rings and Algebras
2025-09-30 v1
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.
Cite
@article{arxiv.2509.22903,
title = {$\chi$ -extending modular lattices},
author = {Jesus Adrian Celis-González and Hugo Alberto Rincón-Mejía},
journal= {arXiv preprint arXiv:2509.22903},
year = {2025}
}