Characteristic ideal
= Characteristic ideal
{title2=$\operatorname{char}_\Lambda M$}
For a finitely generated torsion <Iwasawa module>, its characteristic ideal is the product of the height-one prime ideals raised to the lengths of the corresponding localizations. In the elementary-divisor description it is generated by $p^{\sum a_i}\prod f_j^{b_j}$. It is unchanged by finite modules and multiplicative in <short exact sequences> of torsion modules.