Finite Direct Sum of Noetherian Module is Noetherian

Theorem
Let $A$ be a commutative ring with unity.

Let $n \in \N_{>0}$.

Let $M_1, \ldots, M_n$ be $A$-modules.

Then the direct sum:
 * $\ds \bigoplus_{i \mathop = 1}^n M_i$

is an $A$-Noetherian module.

Proof
By Direct Sum of Modules is Module, it is an $A$-module.

Thus we only need to show that it is Noetherian.