October 20, 2025Open Access

$χ$ -extending modular lattices

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Extending lattices are characterized by two types; type-1 and type-2, which refine modular lattice concepts.
Key relationships are established between essential elements and complements, highlighting modular lattice properties.
Applications of the theory demonstrate its relevance in module theory, suggesting broader mathematical implications.
The study provides foundational definitions and lemmas necessary for deeper exploration of lattice theory.

Implication

This analysis examines extending lattices and modular lattices, suggesting connections to module theory.

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.

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Cite This Study

Celis-González et al. (2025) studied this question.

synapsesocial.com/papers/68f6196ee0bbbc94fac36465 https://doi.org/10.48550/arxiv.2509.22903

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Implication

This analysis examines extending lattices and modular lattices, suggesting connections to module theory.

$χ$ -extending modular lattices

Key Points

Implication

Abstract

Discussion

Cite This Study

$χ$ -extending modular lattices

Key Points

Implication

Abstract

Discussion

Cite This Study

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