Linearly Compact Rings and Modules.
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 cohomology...
Let be a divisor on a smooth algebraic variety . We investigate the geometry of the Jacobian scheme of , homological invariants derived from logarithmic differential forms along , and their relationship with the property that be a free divisor. We consider arrangements of hyperplanes as a source of examples and counterexamples. In particular, we make a complete calculation of the local cohomology of logarithmic forms of generic hyperplane arrangements.
Let be a simple strange Lie superalgebra over the complex field . In a paper by A. Ayupov, K. Kudaybergenov (2016), the authors studied the local derivations on semi-simple Lie algebras over and showed the difference between the properties of local derivations on semi-simple and nilpotent Lie algebras. We know that Lie superalgebras are a generalization of Lie algebras and the properties of some Lie superalgebras are similar to those of semi-simple Lie algebras, but is an exception. In this...
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.