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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 :

 
  1. $Z$ is finite and $X/Z$ has no nonzero, finite $\Lambda-$submodules.

    $Z$ is finite and $X/Z$ has no nonzero, finite $\Lambda-$submodules.

  2. $Y$ is annihilated by a power of $p$ and $X/Y$ is a free $\mathbb Z_p-$module of finite rank.

  1. $Y$ 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 $\mu$)

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 :

 
  1. $Z$ is finite and $X/Z$ has no nonzero, finite $\Lambda-$submodules.
  1. $Y$ 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 $\mu$)

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 :

  1. $Z$ is finite and $X/Z$ has no nonzero, finite $\Lambda-$submodules.

  2. $Y$ 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 $\mu$)

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Iwasawa's invariants

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 :

  1. $Z$ is finite and $X/Z$ has no nonzero, finite $\Lambda-$submodules.
  1. $Y$ 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 $\mu$)