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Let K, L be algebraic number fields with K ⊆ L, and , their respective rings of integers. We consider the trace map
and the -ideal . By I(L/K) we denote the group indexof in (i.e., the norm of over ℚ). It seems to be difficult to determine I(L/K) in the general case. If K and L are absolutely abelian number fields, however, we obtain a fairly explicit description of the number I(L/K). This is a consequence of our description of the Galois module structure of (Theorem 1). The case...
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