FBN Modules

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-bo...

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Bibliographic Details
Published in:Communications in algebra 2012-12, Vol.40 (12), p.4604-4616
Main Authors: Pérez, Jaime Castro, Montes, José Ríos
Format: Article
Language:English
Subjects:
Ideal invariant torsion theory
M-ideal
Prime submodules
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Summary: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.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2011.613879