2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/108841In cyclic, degree 8 extensions of algebraic number fields $N/K$, ambiguous ideals in N are canonical $\mathbb{Z}[C_8]$-modules. Their $\mathbb{Z}[C_8]$-structure is determined here. It is described in terms of indecomposable modules and determined by ramification invariants. Although infinitely many indecomposable $\mathbb{Z}[C_8]$-modules are available (classification by Yakovlev), only 23 appear.This article has appeared in the Lect. Notes Pure Appl. Math. without references. The article is being posted here, with permission, to remedy that problemNumber Theory11S23; 20C10text