Modules of finite length are finite.

Lemma 10.52.2. Let $R$ be a ring. Let $M$ be an $R$-module. If $\text{length}_ R(M) < \infty$ then $M$ is a finite $R$-module.

Proof. Omitted. $\square$

Comment #1368 by Herman Rohrbach on

Suggested slogan: Modules of finite length are finite.

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