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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Localization and colocalization in tilting torsion theory for coalgebras

Yuan Li, Hailou Yao (2021)

Czechoslovak Mathematical Journal

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Tilting theory plays an important role in the representation theory of coalgebras. This paper seeks how to apply the theory of localization and colocalization to tilting torsion theory in the category of comodules. In order to better understand the process, we give the (co)localization for morphisms, (pre)covers and special precovers. For that reason, we investigate the (co)localization in tilting torsion theory for coalgebras.