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

f -derivations on rings and modules

Paul E. Bland (2006)

Commentationes Mathematicae Universitatis Carolinae

Similarity:

If τ is a hereditary torsion theory on 𝐌𝐨𝐝 R and Q τ : 𝐌𝐨𝐝 R → 𝐌𝐨𝐝 R is the localization functor, then we show that every f -derivation d : M → N has a unique extension to an f τ -derivation d τ : Q τ ( M ) → 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 → 𝐌𝐨𝐝 R is the colocalization functor, then every f -derivation d : M → N can be lifted uniquely to an f τ -derivation d τ : C τ ( M ) → C τ ( N ) .

On torsionfree classes which are not precover classes

Ladislav Bican (2008)

Czechoslovak Mathematical Journal

Similarity:

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...

Local cohomology in classical rings.

José Luis Bueso Montero, Pascual Jara Martínez (1992)

Publicacions Matemàtiques

Similarity:

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...