Theorems · Theorem · number theory
FractionalIdeal.absNorm_div_norm_eq_absNorm_div_norm
∀ {R : Type u_1} [inst : CommRing R] [inst_1 : IsDedekindDomain R] [inst_2 : Module.Free ℤ R] [Module.Finite ℤ R]
{K : Type u_2} [inst_4 : CommRing K] [inst_5 : Algebra R K] [IsFractionRing R K]
{I : FractionalIdeal (nonZeroDivisors R) K} (a : ↥(nonZeroDivisors R)) (I₀ : Ideal R),
a • ↑I = Submodule.map (Algebra.linearMap R K) I₀ →
↑(Ideal.absNorm I.num) / ↑|(Algebra.norm ℤ) ↑I.den| = ↑(Ideal.absNorm I₀) / ↑|(Algebra.norm ℤ) ↑a|- Defined in
- Mathlib.RingTheory.FractionalIdeal.Norm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 157 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites38
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.idstatement · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Submodulestatement and proof · cited by 7,192
- Idealstatement and proof · cited by 4,748
- MonoidHomstatement · cited by 3,629
- Submonoidstatement · cited by 3,086
- mul_commproof · cited by 2,262
- absstatement · cited by 1,814
- map_mulproof · cited by 1,137
- Module.Finitestatement and proof · cited by 1,032
Cited by1
Results whose statement or proof uses this declaration.
- FractionalIdeal.absNorm_eq'proof · cited by 2