Iwasawa invariants
= Iwasawa invariants
{c}
{title2=$\mu(M)=\sum_i a_i,\quad\lambda(M)=\sum_j b_j\deg f_j$}
The invariants $\mu,\lambda$ of a finitely generated torsion <Iwasawa module> measure its $p$-power elementary factors and distinguished-polynomial factors. Vanishing of $\mu$ means that the module is finitely generated over $\mathbb Z_p$, up to finite error. It does not mean that the module is finite: a factor $\Lambda/(T)$ has $\mu=0$ and is $\mathbb Z_p$.