I want a reference that treated the proof of this proposition :
Proposition : Suppose that $X$ is a finitely generated, torsion $\Lambda-$module. Then there are uniquely determined $\Lambda-$submodules $Z$ and $Y$ of $X$ with the following properties :
- $Z$ is finite and $X/Z$ has no nonzero, finite $\Lambda-$submodules.
$Z$ is finite and $X/Z$ has no nonzero, finite $\Lambda-$submodules.
$Y$ is annihilated by a power of $p$ and $X/Y$ is a free $\mathbb Z_p-$module of finite rank.
- $Y$ is annihilated by a power of $p$ and $X/Y$ is a free $\mathbb Z_p-$module of finite rank.
Or someone help me to prove.This proposition allows us to define certain Iwasawa's invariants ($\lambda$ and $\mu$)