= Iwasawa module structure theorem
{c}
A finitely generated <module> over $\Lambda=\mathbb Z_p[[T]]$ is <pseudo-isomorphic> to
$$
\Lambda^r\oplus\bigoplus_i\Lambda/(p^{a_i})\oplus\bigoplus_j\Lambda/(f_j^{b_j}),
$$
where the $f_j$ are irreducible <distinguished polynomials>. Height-one localizations are discrete valuation rings, which give the elementary divisors; the remaining errors are supported only at the maximal ideal and are finite. This is a finite-error classification, not necessarily an actual direct-sum decomposition.
Back to article page
