$χ$ -extending modular lattices
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866914058817503232 |
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| author | Celis-González, Jesus Adrian Rincón-Mejía, Hugo Alberto |
| author_facet | Celis-González, Jesus Adrian Rincón-Mejía, Hugo Alberto |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_22903 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $χ$ -extending modular lattices Celis-González, Jesus Adrian Rincón-Mejía, Hugo Alberto Rings and Algebras 06C05, 06B35, 06C15, 06C20 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. |
| title | $χ$ -extending modular lattices |
| topic | Rings and Algebras 06C05, 06B35, 06C15, 06C20 |
| url | https://arxiv.org/abs/2509.22903 |