What does it mean that the relative discriminant is generated by a unit?

asked 2019-12-16 18:17:21 +0200

julio gravatar image

updated 2019-12-23 16:58:57 +0200

Iguananaut gravatar image

Does it mean that there is no relative integral basis?

sage: alpha=sqrt(-17/2 + sqrt(17^2-4(17))/2)
sage: f=alpha.minpoly()
sage: K.<a>=NumberField(x^4+17*x^2+17)
sage: R<y>=PolynomialRing(K)
sage: R(f).factor()

sage: g=y^2+a^2+17
sage: L.<b>=K.extension(g)
sage: L.relative_discriminant()
Fractional ideal (1)
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Probably yes, but it would be better to ask this math question on math.stackexchange.com.

rburing gravatar imagerburing ( 2019-12-17 15:32:56 +0200 )edit