A remark on relative integral bases for infinite extensions of finite number fields

Abstract

Let K be a finite algebraic extension of the rational number field Q , and let R denote the ring of algebraic integers in K . The algebraic integers in a finite extension field of K form a ring which may be considered as a module over R . The structure of these modules has been entirely determined in Frohlich [2], where, in particular, necessary and sufficient conditions have been established deciding when such a module will be a free R -module.