Theorems · Theorem · number theory

NumberField.absNorm_differentIdeal

∀ (K : Type u_1) (𝒪 : Type u_2) [inst : Field K] [inst_1 : NumberField K] [inst_2 : CommRing 𝒪] [inst_3 : Algebra 𝒪 K]
  [IsFractionRing 𝒪 K] [inst_5 : IsDedekindDomain 𝒪] [inst_6 : CharZero 𝒪] [inst_7 : Module.Finite ℤ 𝒪],
  Ideal.absNorm (differentIdeal ℤ 𝒪) = (NumberField.discr K).natAbs

Defined in: Mathlib.NumberTheory.NumberField.Discriminant.Different
Cited by: 4 results in Mathlib
Foundations: Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField CommRing Algebra IsFractionRing IsDedekindDomain CharZero Module.Finite

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Cites105

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
RingHom.idproof · cited by 18,349
CommRingstatement and proof · cited by 17,173
Algebrastatement and proof · cited by 11,388
Top.topproof · cited by 9,680
Fintypeproof · cited by 7,736
Fieldstatement and proof · cited by 7,404
Submoduleproof · cited by 7,192
Idealstatement · cited by 4,748
Algebra.algebraMapproof · cited by 4,706
Set.rangeproof · cited by 4,705
AddGroupproof · cited by 4,410

Cited by4

Results whose statement or proof uses this declaration.

NumberField.not_dvd_discr_iff_forall_liesOverproof · cited by 2
NumberField.natAbs_discr_eq_absNorm_differentIdeal_mul_natAbs_discr_powproof · cited by 2
NumberField.discr_mem_differentIdealproof · cited by 1
NumberField.natAbs_discr_eq_natAbs_discr_pow_mul_natAbs_discr_powproof · cited by 1