Modules With Unique Closure Relative to a Torsion Theory II
We study modules M over a general ring R such that every submodule has a unique closure with respect to a hereditary torsion theory t on Mod-R using the fact that the module M satisfies a certain transitivity property on t-closed submodules.
Anahtar Kelimeler:
Closed submodule, UC-module, hereditary torsion theory.
Modules With Unique Closure Relative to a Torsion Theory II
We study modules M over a general ring R such that every submodule has a unique closure with respect to a hereditary torsion theory t on Mod-R using the fact that the module M satisfies a certain transitivity property on t-closed submodules.
Keywords:
Closed submodule, UC-module, hereditary torsion theory.,
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- Moreover, in this case N+is the unique τ -closure of N in M , for every submodule N of M . Proof. For the equivalence of (1) - (12) see Lemmas 2.3, 2.4 and 2.6 and Corollary 2.5. Now suppose that M is a τ -U C -module. Let N be any submodule of M . Then N+is the unique τ -closure of N in M by the proof of Lemma 2.6.
- ISSN: 1300-0098
- Yayın Aralığı: Yılda 6 Sayı
- Yayıncı: TÜBİTAK
Sayıdaki Diğer Makaleler
Modules With Unique Closure Relative to a Torsion Theory II
On $tau$-lifting modules and $tau$-semiperfect modules
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