MTame Modules And Local Gabriel Correspondence

Using the concept of prime submodule for M ∈ R-Mod, P ∈ Spec(M), and N ∈ σ[M], we define when N is P-Mtame \ (Mtame) module. This concept generalizes the concept\ of P-tame (tame) modules. For M ∈ R-Mod and τ ∈M-tors, we use the concept of τ M -Gabriel dimension and we study the relationship between...

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Bibliographic Details
Published in:Communications in algebra 2015-10, Vol.43 (10), p.4471-4486
Main Authors: Pérez, Jaime Castro, Montes, José Ríos
Format: Article
Language:English
Subjects:
Gabriel correspondence
Krull dimension
Prime submodules
Tame modules
Torsion theory
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Summary:Using the concept of prime submodule for M ∈ R-Mod, P ∈ Spec(M), and N ∈ σ[M], we define when N is P-Mtame \ (Mtame) module. This concept generalizes the concept\ of P-tame (tame) modules. For M ∈ R-Mod and τ ∈M-tors, we use the concept of τ M -Gabriel dimension and we study the relationship between Mtame modules and τ M -Gabriel dimension. We find equivalent conditions for a module M progenerator in σ[M] with τ M -Gabriel dimension to have τ M -Gabriel correspondence in terms of the P-Mtame modules. This result extends the results by Albu et al. and Kim and Krause.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2014.946609