Theorems · Theorem · number theory
FractionalIdeal.absNorm_eq
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] [inst_2 : Module.Free ℤ R]
[inst_3 : Module.Finite ℤ R] {K : Type u_2} [inst_4 : CommRing K] [inst_5 : Algebra R K] [inst_6 : IsFractionRing R K]
(I : FractionalIdeal (nonZeroDivisors R) K),
FractionalIdeal.absNorm I = ↑(Ideal.absNorm I.num) / ↑|(Algebra.norm ℤ) ↑I.den|- Defined in
- Mathlib.RingTheory.FractionalIdeal.Norm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealstatement · cited by 4,748
- MonoidHomstatement · cited by 3,629
- Submonoidstatement · cited by 3,086
- absstatement · cited by 1,814
- Module.Finitestatement and proof · cited by 1,032
- nonZeroDivisorsstatement and proof · cited by 895
- IsFractionRingstatement and proof · cited by 738
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement and proof · cited by 668
Cited by2
Results whose statement or proof uses this declaration.
- FractionalIdeal.abs_det_basis_changeproof · cited by 1
- FractionalIdeal.absNorm_eq_zero_iffproof · cited by 0