Statement: Let $R$ be a semiprimary ring. Then for an $R$ module $M$, the following are equivalent: 1) $M$ is Noetherian; 2) $M$ is Artinian; 3) $M$ has a finite composition series.

Link: https://en.wikipedia.org/wiki/Hopkins%E2%80%93Levitzki_theorem

- T.-Y. Lam. A first course in noncommutative rings. (2013) @ Theorem 4.15 pp 55-56