Theorems · Theorem · algebraic geometry
PrimeSpectrum.isClosed_iff_zeroLocus_radical_ideal
∀ {R : Type u} [inst : CommSemiring R] (Z : Set (PrimeSpectrum R)),
IsClosed Z ↔ ∃ I, I.IsRadical ∧ Z = PrimeSpectrum.zeroLocus ↑I- Cited by
- 0 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites12
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.coestatement and proof · cited by 8,199
- Idealstatement and proof · cited by 4,748
- IsClosedstatement · cited by 1,639
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- Ideal.radicalproof · cited by 121
- Ideal.IsRadicalstatement and proof · cited by 30
- Ideal.radical_isRadicalproof · cited by 7
- PrimeSpectrum.zeroLocus_radicalproof · cited by 6
- PrimeSpectrum.isClosed_iff_zeroLocus_idealproof · cited by 4
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