Theorems · Theorem · commutative algebra
Ideal.spanNorm_le_comap
∀ (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] (I : Ideal S), Ideal.spanNorm R I ≤ Ideal.comap (algebraMap R S) I- Defined in
- Mathlib.RingTheory.Ideal.Norm.RelNorm
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 187 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Set.imageproof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- Submodule.spanproof · cited by 1,504
- Module.Finitestatement and proof · cited by 1,032
- Module.IsTorsionFreestatement and proof · cited by 600
Cited by1
Results whose statement or proof uses this declaration.
- Ideal.relNorm_le_comapproof · cited by 0