The Galois Structure of Ambiguous Ideals in Cyclic Extensions of Degree 8

Abstract

Abstract. In cyclic, degree 8 extensions of algebraic number fields N/K, ambiguous ideals in N are canonical Z[C 8 ]-modules. Their Z[C 8 ]-structure is determined here. It is described in terms of indecomposable modules and determined by ramification invariants. Although infinitely many indecomposable Z[C 8 ]-modules are available (classification by Yakovlev), only 23 appear.