Czechoslovak Mathematical Journal, Vol. 70, No. 1, pp. 121-145, 2020
The torsion theory and the Melkersson condition
Received April 30, 2018. Published online September 18, 2019.
Abstract: 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 condition appears in the context of torsion theories.
Keywords: Melkersson condition; Serre subcategory; torsion theory