Theorems · Theorem · commutative algebra
Ideal.map_spanIntNorm
∀ (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) {T : Type u_4} [inst_9 : Semiring T] (f : R →+* T),
Ideal.map f (Ideal.spanNorm R I) = Ideal.span (⇑f ∘ ⇑(Algebra.intNorm R S) '' ↑I)- Defined in
- Mathlib.RingTheory.Ideal.Norm.RelNorm
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 186 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites20
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
- CommRingstatement and proof · cited by 17,173
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- SetLike.coestatement and proof · cited by 8,199
- Set.imagestatement and proof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- MonoidHomstatement · cited by 3,629
- IsDomainstatement and proof · cited by 2,196
- Module.Finitestatement and proof · cited by 1,032
- Ideal.spanstatement and proof · cited by 948
Cited by2
Results whose statement or proof uses this declaration.
- Ideal.spanIntNorm_localizationproof · cited by 3
- Ideal.map_relNormproof · cited by 0