Theorems · Theorem · algebraic geometry
PrimeSpectrum.closure_image_comap_zeroLocus
∀ {R : Type u_1} {S : Type u_2} [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S) (I : Ideal S),
closure (PrimeSpectrum.comap f '' PrimeSpectrum.zeroLocus ↑I) = PrimeSpectrum.zeroLocus ↑(Ideal.comap f I)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 83 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites30
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · 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
- closurestatement · cited by 1,254
- Ideal.IsPrimeproof · cited by 827
- PrimeSpectrumstatement and proof · cited by 625
- Ideal.comapstatement and proof · cited by 443
- PrimeSpectrum.asIdealproof · cited by 333
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isIntegral_of_isClosedMap_comap_mapRingHomproof · cited by 1