Abstract
For an algebraic number field [Formula: see text], let [Formula: see text] denote the discriminant of an algebraic number field [Formula: see text]. It is well known that if [Formula: see text] are algebraic number fields with coprime discriminants, then [Formula: see text] are linearly disjoint over the field [Formula: see text] of rational numbers and [Formula: see text], [Formula: see text] being the degree of [Formula: see text] over [Formula: see text]. In this paper, we prove that the converse of this result holds in relative extensions of algebraic number fields. We also give some more necessary and sufficient conditions for the analogue of the above equality to hold for algebraic number fields [Formula: see text] linearly disjoint over [Formula: see text].
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