Theorems · Theorem · algebraic geometry
PrimeSpectrum.closure_singleton
∀ {R : Type u} [inst : CommSemiring R] (x : PrimeSpectrum R), closure {x} = PrimeSpectrum.zeroLocus ↑x.asIdeal- Cited by
- 0 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites10
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
- closurestatement · cited by 1,254
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealstatement and proof · cited by 333
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closureproof · cited by 11
- PrimeSpectrum.vanishingIdeal_singletonproof · cited by 5
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