Lemma 15.88.5. Let I be a finitely generated ideal of a ring R. The I-power torsion modules form a Serre subcategory of the abelian category \text{Mod}_ R, see Homology, Definition 12.10.1.
Proof. It is clear that a submodule and a quotient module of an I-power torsion module is I-power torsion. Moreover, the extension of two I-power torsion modules is I-power torsion by Lemma 15.88.4. Hence the statement of the lemma by Homology, Lemma 12.10.2. \square
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