Theorems · Theorem · algebraic geometry

image_comap_zeroLocus_eq_zeroLocus_comap

∀ {R : Type u} (S : Type v) [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S),
  Function.Surjective ⇑f →
    ∀ (I : Ideal S), PrimeSpectrum.comap f '' PrimeSpectrum.zeroLocus ↑I = PrimeSpectrum.zeroLocus ↑(Ideal.comap f I)

Defined in: Mathlib.RingTheory.Spectrum.Prime.RingHom
Cited by: 1 results in Mathlib
Foundations: Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing CommRing

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites29

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
Setstatement · cited by 53,352
CommRingstatement and proof · cited by 17,173
RingHomstatement and proof · cited by 10,189
SetLike.coestatement and proof · cited by 8,199
Set.imagestatement · cited by 5,609
Idealstatement and proof · cited by 4,748
LE.le.transproof · cited by 3,151
Ideal.mapproof · cited by 692
PrimeSpectrumstatement and proof · cited by 625
map_subproof · cited by 565
Ideal.comapstatement and proof · cited by 443

Cited by1

Results whose statement or proof uses this declaration.

range_comap_of_surjectiveproof · cited by 9