Short Exact Sequence Condition of Noetherian Modules

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

Let:
 * $0 \longrightarrow M' \stackrel {\alpha} {\longrightarrow} M \stackrel {\beta} {\longrightarrow} M'' \longrightarrow 0$

be a short exact sequence of $A$-modules.

Then:
 * $M$ is Noetherian


 * $M'$ and $M''$ are Noetherian
 * $M'$ and $M''$ are Noetherian