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.

中文翻译：

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扭转理论和梅尔克森条件

我们考虑对扭转理论概念的推广，该理论与可交换诺特环上的 Serre 子范畴相关联。2008 年，Aghapournahr 和 Melkersson 研究了局部上同调模块何时属于模块类别的 Serre 子类别的问题。在他们的研究中，Melkersson 条件的概念被定义为局部上同调理论中的一个合适的条件。我们在本文中的目的之一是展示 Melkersson 条件的概念在扭转理论的背景下是如何自然出现的。