Theorems · Theorem · commutative algebra
Ideal.relNorm_relNorm
∀ (R : Type u_1) [inst : CommRing R] [inst_1 : IsDomain R] {S : Type u_3} [inst_2 : CommRing S] [inst_3 : IsDomain S]
[inst_4 : IsIntegrallyClosed R] [inst_5 : IsIntegrallyClosed S] [inst_6 : Algebra R S] [inst_7 : Module.Finite R S]
[inst_8 : Module.IsTorsionFree R S] [inst_9 : IsDedekindDomain R] [inst_10 : IsDedekindDomain S] (T : Type u_4)
[inst_11 : CommRing T] [inst_12 : IsDedekindDomain T] [inst_13 : IsIntegrallyClosed T] [inst_14 : Algebra R T]
[inst_15 : Algebra T S] [IsScalarTower R T S] [inst_17 : Module.Finite R T] [inst_18 : Module.Finite T S]
[inst_19 : Module.IsTorsionFree R T] [inst_20 : Module.IsTorsionFree T S] (I : Ideal S),
(Ideal.relNorm R) ((Ideal.relNorm T) I) = (Ideal.relNorm R) I- Defined in
- Mathlib.RingTheory.Ideal.Norm.RelNorm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 191 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 and proof · cited by 4,748
- IsScalarTowerstatement and proof · cited by 3,896
- IsDomainstatement and proof · cited by 2,196
- Module.Finitestatement and proof · cited by 1,032
- MonoidWithZeroHomstatement · cited by 704
- IsDedekindDomainstatement and proof · cited by 668
- Module.IsTorsionFreestatement and proof · cited by 600
- IsIntegrallyClosedstatement and proof · cited by 203
- Ideal.relNormstatement · cited by 23
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.absNorm_algebraMapproof · cited by 2
- Ideal.relNorm_eq_pow_of_isMaximalproof · cited by 1