Let $A$ be a ring and $M_1,\dots ,M_n$ be $A$-modules. Then $\underset{i=1}{\overset{n}{⨁}}{M}_i$ is Noetherian/Artinian iff 1;; each $M_i$ is Noetherian/Artinian

Uses:

• 6. Proposition 4.6.3 - Noetherian respects exactness