Integral bases for subfields of cyclotomic fields (Q1361006)

The standard integral basis \(B_n = \{1, \zeta, \ldots, \zeta^{\phi(n)-1}\}\) for the field of \(n\)-th roots of unity does not have the property that \(B_m \subset B_n\) for \(m \mid n\). \textit{W. Bosma} [Appl. Algebra Eng. Commun. Comput. 1, 125-134 (1990; Zbl 0741.11041)] has constructed integral bases with this property. The author presents a different solution to this problem which was developed in an unpublished thesis by Zumbroich. He also considers relative integral bases over cyclotomic fields and points out the relevance to computations with matrix representations.