Displaying similar documents to “The torsion problem of H.-J. Reiffen and U. Vetter”

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...

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.

The torsion theory and the Melkersson condition

Takeshi Yoshizawa (2020)

Czechoslovak Mathematical Journal

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We consider a generalization of the notion of torsion theory, which is associated with a Serre subcategory over a commutative Noetherian ring. In 2008 Aghapournahr and Melkersson investigated the question of when local cohomology modules belong to a Serre subcategory of the module category. In their study, the notion of Melkersson condition was defined as a suitable condition in local cohomology theory. One of our purposes in this paper is to show how naturally the concept of Melkersson...