MTame Modules And Local Gabriel Correspondence

Abstract

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.

Key Words:

• Gabriel correspondence
• Krull dimension
• Prime submodules
• Tame modules
• Torsion theory

2010 Mathematics Subject Classification:

• 16S90
• 16D50
• 16P50
• 16P70

Notes

Communicated by T. Albu