A Note on Gabriel dimension for idioms
Angel Zald\'ivar
TL;DR
This paper clarifies that the Gabriel dimension for modular lattices aligns with the module case, emphasizing the consistency in its definition and construction across these mathematical structures.
Contribution
It demonstrates the equivalence of Gabriel dimension definitions for modular lattices and modules, extending existing theory to unify these concepts.
Findings
Gabriel dimension for modular lattices matches that for modules.
The construction method is consistent across both contexts.
Provides a unified perspective on Gabriel dimension in lattice and module theory.
Abstract
The aim of this note is to illustrate that the definition and construction of the Gabriel dimension for modular lattices in the classical sense is the same as the module case following H. Simmons.
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Taxonomy
TopicsRings, Modules, and Algebras · Advanced Topics in Algebra · Fuzzy and Soft Set Theory