Theorems · Theorem · algebraic geometry
PrimeSpectrum.zeroLocus_subset_zeroLocus_singleton_iff
∀ {R : Type u} [inst : CommSemiring R] (f g : R),
PrimeSpectrum.zeroLocus {f} ⊆ PrimeSpectrum.zeroLocus {g} ↔ g ∈ (Ideal.span {f}).radical- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- CommSemiringstatement and proof · cited by 10,911
- SetLike.coeproof · cited by 8,199
- Idealstatement · cited by 4,748
- Ideal.spanstatement and proof · cited by 948
- PrimeSpectrumstatement and proof · cited by 625
- SetLike.mem_coeproof · cited by 302
- Set.singleton_subset_iffproof · cited by 206
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- Ideal.radicalstatement and proof · cited by 121
- Ideal.span_leproof · cited by 70
- PrimeSpectrum.zeroLocus_spanproof · cited by 17
Cited by1
Results whose statement or proof uses this declaration.
- PrimeSpectrum.basicOpen_le_basicOpen_iffproof · cited by 0