= Characteristic series of an Iwasawa module
{title2=$\operatorname{char}_{\mathbb Z_p[[S]]}(M)=(f_M(S))$}
= Characteristic series
{synonym}
= Characteristic power series
{synonym}
For a finitely generated torsion <Iwasawa module>, this is a generator of its <characteristic ideal>, unique up to a <unit> of the <formal power series> ring. It may be chosen as a power of $p$ times a product of distinguished polynomials. The series itself and the ideal it generates are different objects; changing a generator by a <unit> preserves the ideal. When the finite <Euler characteristic of a one-variable Iwasawa module> is defined, the inverse p-adic absolute value of its constant term gives that invariant.
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