Theorems · Theorem · algebraic geometry
range_comap_of_surjective
∀ {R : Type u} (S : Type v) [inst : CommRing R] [inst_1 : CommRing S] (f : R →+* S),
Function.Surjective ⇑f → Set.range (PrimeSpectrum.comap f) = PrimeSpectrum.zeroLocus ↑(RingHom.ker f)- Cited by
- 9 results in Mathlib
- Foundations
- Depth 69 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
- Setstatement and proof · cited by 53,352
- CommRingstatement and proof · cited by 17,173
- CommSemiringproof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- SetLike.coestatement and proof · cited by 8,199
- Set.imageproof · cited by 5,609
- Idealstatement and proof · cited by 4,748
- Bot.botproof · cited by 4,720
- Set.rangestatement · cited by 4,705
- Set.univproof · cited by 3,945
- SetLikeproof · cited by 1,084
Cited by9
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isConstructible_comap_imageproof · cited by 3
- PrimeSpectrum.isClosed_range_comap_of_surjectiveproof · cited by 2
- PrimeSpectrum.comap_evalRingHom_basicOpenproof · cited by 2
- AlgebraicGeometry.Scheme.IdealSheafData.range_glueDataObjιproof · cited by 1
- PrimeSpectrum.comap_quotientMk_bijective_of_le_nilradicalproof · cited by 1
- PrimeSpectrum.exists_range_eq_of_isConstructibleproof · cited by 1
- AlgebraicGeometry.isOpenImmersion_SpecMap_iff_of_surjectiveproof · cited by 0
- chevalley_mvPolynomial_mvPolynomialproof · cited by 0