Higher derivations on rings and modules.

Bland, Paul E.

Displaying similar documents to “Higher derivations on rings and modules.”

$f$ -derivations on rings and modules

Paul E. Bland (2006)

Commentationes Mathematicae Universitatis Carolinae

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If $τ$ is a hereditary torsion theory on ${𝐌𝐨𝐝}_{R}$ and $Q_{τ} : {𝐌𝐨𝐝}_{R} \to {𝐌𝐨𝐝}_{R}$ is the localization functor, then we show that every $f$ -derivation $d : M \to N$ has a unique extension to an $f_{τ}$ -derivation $d_{τ} : Q_{τ} (M) \to Q_{τ} (N)$ when $τ$ is a differential torsion theory on ${𝐌𝐨𝐝}_{R}$ . Dually, it is shown that if $τ$ is cohereditary and $C_{τ} : {𝐌𝐨𝐝}_{R} \to {𝐌𝐨𝐝}_{R}$ is the colocalization functor, then every $f$ -derivation $d : M \to N$ can be lifted uniquely to an $f_{τ}$ -derivation $d_{τ} : C_{τ} (M) \to C_{τ} (N)$ .

Rings admitting torsion injective covers

Ahsan, J., Enochs, E. (1981)

Portugaliae mathematica

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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...

Abelian groups in a topos of sheaves: Torsion and essential extensions.

Bhutani, Kiran R. (1989)

International Journal of Mathematics and Mathematical Sciences

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Local cohomology in classical rings.

José Luis Bueso Montero, Pascual Jara Martínez (1992)

Publicacions Matemàtiques

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The aim of this paper is to establish the close connection between prime ideals and torsion theories in a non necessarily commutative noetherian ring. We introduce a new definition of support of a module and characterize some kinds of torsion theories in terms of prime ideals. Using the machinery introduced before, we prove a version of the Mayer-Vietoris Theorem for local cohomology and establish a relationship between the classical dimension and the vanishing of the groups of local...

Characterization of the torsion of the Jacobian of y² = x⁵+Ax and some applications

Tomasz Jędrzejak, Maciej Ulas (2010)

Acta Arithmetica

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Cotorsion modules for torsion theories

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

Portugaliae mathematica

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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...