The discriminant of compositum of algebraic number fields.

For an algebraic number field K , let d K denote the discriminant of an algebraic number field K. It is well known that if K 1 , K 2 are algebraic number fields with coprime discriminants, then K 1 , K 2 are linearly disjoint over the field ℚ of rational numbers and d K 1 K 2 = d K 1 n 2 d K 2 n 1 , n i being the degree of K i over ℚ. 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 K 1 , K 2 linearly disjoint over K 1 ∩ K 2 . [ABSTRACT FROM AUTHOR]