Let $p$ be a prime and $M$ is a finitely generated $ \mathbb{Z}_{p}[[T]] $ module. Suppose $N$ denotes the torsion of $M$. Then $N$ and $M/(p)$ are both $ F_{p} $ vector spaces. So we can talk of their dimensions. Now what can we say about rank of $M$ from looking at the dimensions of $N$ and $M/(p) ?$