The Torsion Theory and the Melkersson Condition


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.

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The author expresses gratitude to the referees for their kind comments and valuable suggestions.

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Correspondence to Takeshi Yoshizawa.

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Yoshizawa, T. The Torsion Theory and the Melkersson Condition. Czech Math J 70, 121–145 (2020).

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  • Melkersson condition
  • Serre subcategory
  • torsion theory

MSC 2010

  • 13C60
  • 13D30