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Cotorsion Theories Cogenerated by a Torsionfree Class.
- Source :
-
Communications in Algebra . Nov2011, Vol. 39 Issue 11, p3981-3992. 12p. - Publication Year :
- 2011
-
Abstract
- Let R be a right perfect ring, and let (ℱ, 𝒞) be a cotorsion theory in the category of right R-modules ℳ R . In this article, it is shown that every right R-module has a superfluous ℱ-cover if and only if there exists a torsion theory (𝒜, ℬ) such that (ℱ, 𝒞) is cogenerated by ℬ. It is also proved that if (𝒜, ℬ) is a cosplitting torsion theory, then (⊥ℬ, (⊥ℬ)⊥) is a hereditary and complete cotorsion theory, and if (𝒜, ℬ) is a centrally splitting torsion theory, then (⊥ℬ, (⊥ℬ)⊥) is a hereditary and perfect cotorsion theory. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00927872
- Volume :
- 39
- Issue :
- 11
- Database :
- Academic Search Index
- Journal :
- Communications in Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 67366631
- Full Text :
- https://doi.org/10.1080/00927872.2010.515636