Weak Baer modules over graded rings

Mark Teply; Blas Torrecillas

Displaying similar documents to “Weak Baer modules over graded rings”

Strongly graded left FTF rings.

José Gómez, Blas Torrecillas (1992)

Publicacions Matemàtiques

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An associated ring R with identity is said to be a left FTF ring when the class of the submodules of flat left R-modules is closed under injective hulls and direct products. We prove (Theorem 3.5) that a strongly graded ring R by a locally finite group G is FTF if and only if R is left FTF, where e is a neutral element of G. This provides new examples of left FTF rings. Some consequences of this Theorem are given.

Stable Clifford theory for divisorially graded rings.

Gómez Torrecillas, José, Torrecillas, Blas (1994)

Bulletin of the Belgian Mathematical Society - Simon Stevin

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Cotorsion modules for torsion theories

Henderson, J., Orzech, M. (1977)

Portugaliae mathematica

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Relative exact covers

Ladislav Bican, Blas Torrecillas (2001)

Commentationes Mathematicae Universitatis Carolinae

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Recently Rim and Teply [11] found a necessary condition for the existence of $σ$ -torsionfree covers with respect to a given hereditary torsion theory for the category $R$ -mod. This condition uses the class of $σ$ -exact modules; i.e. the $σ$ -torsionfree modules for which every its $σ$ -torsionfree homomorphic image is $σ$ -injective. In this note we shall show that the existence of $σ$ -torsionfree covers implies the existence of $σ$ -exact covers, and we shall investigate some sufficient conditions for...

Extending modules relative to a torsion theory

Semra Doğruöz (2008)

Czechoslovak Mathematical Journal

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An $R$ -module $M$ is said to be an extending module if every closed submodule of $M$ is a direct summand. In this paper we introduce and investigate the concept of a type 2 $τ$ -extending module, where $τ$ is a hereditary torsion theory on $Mod$ - $R$ . An $R$ -module $M$ is called type 2 $τ$ -extending if every type 2 $τ$ -closed submodule of $M$ is a direct summand of $M$ . If $τ_{I}$ is the torsion theory on $Mod$ - $R$ corresponding to an idempotent ideal $I$ of $R$ and $M$ is a type 2 $τ_{I}$ -extending $R$ -module, then the question of whether...

On torsionfree classes which are not precover classes

Ladislav Bican (2008)

Czechoslovak Mathematical Journal

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In the class of all exact torsion theories the torsionfree classes are cover (precover) classes if and only if the classes of torsionfree relatively injective modules or relatively exact modules are cover (precover) classes, and this happens exactly if and only if the torsion theory is of finite type. Using the transfinite induction in the second half of the paper a new construction of a torsionfree relatively injective cover of an arbitrary module with respect to Goldie’s torsion theory...