Geodesic
The torsion theory and the Melkersson condition
Czechoslovak Mathematical Journal, Tome 70 (2020) no. 1, pp. 121-145 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 condition appears in the context of torsion theories.
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.
DOI : 10.21136/CMJ.2019.0193-18
Classification : 13C60, 13D30
Keywords: Melkersson condition; Serre subcategory; torsion theory 
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Yoshizawa, Takeshi. The torsion theory and the Melkersson condition. Czechoslovak Mathematical Journal, Tome 70 (2020) no. 1, pp. 121-145. doi: 10.21136/CMJ.2019.0193-18

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