FBN Modules

Abstract

For M ∈ R-Mod and τ ∈M-tors, we define the concept of fully τ-bounded module as a generalization of the concept of fully τ-bounded ring. We prove that for a τ-noetherian module M with local τ _M -Gabriel correspondence, which is a progenerator of σ[M] and with τ is FIS-invariant, then M is fully τ-bounded. Also, we show that if M is τ-noetherian and fully τ-bounded, then M has local τ _M -Gabriel correspondence.

Key Words:

• Ideal invariant torsion theory
• M-ideal
• Prime submodules

2010 Mathematics Subject Classification:

• 16S90
• 16D50
• 16P50
• 16P70

Notes

Communicated by T. Albu.