The relative different δL / K is defined in a similar manner for an extension of number fields L / K. The relative norm of the relative different is then equal to the relative discriminant ΔL / K. In a tower of fields L / K / F the relative differents are related by δL / F = δL / KδK / F.
The relative different equals the annihilator of the relative Kähler differential module :
Read more about this topic: Different Ideal
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