The Stacks project

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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