Theorems · Theorem · algebraic geometry
PrimeSpectrum.denseRange_comap_iff_ker_le_nilRadical
∀ {R : Type u_1} {S : Type u_2} [inst : CommSemiring R] [inst_1 : CommSemiring S] (f : R →+* S),
DenseRange (PrimeSpectrum.comap f) ↔ RingHom.ker f ≤ nilradical R- Cited by
- 1 results in Mathlib
- Foundations
- Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiringCommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement and proof · cited by 10,189
- SetLike.coeproof · cited by 8,199
- Idealstatement · cited by 4,748
- Set.univproof · cited by 3,945
- PrimeSpectrumstatement and proof · cited by 625
- RingHom.kerstatement and proof · cited by 363
- PrimeSpectrum.comapstatement · cited by 199
- DenseRangestatement · cited by 164
- SetLike.coe_subset_coeproof · cited by 53
- nilradicalstatement and proof · cited by 41
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.denseRange_comap_iff_minimalPrimesproof · cited by 0