Theorems · Theorem · algebraic geometry
PrimeSpectrum.vanishingIdeal_union
∀ {R : Type u} [inst : CommSemiring R] (t t' : Set (PrimeSpectrum R)),
PrimeSpectrum.vanishingIdeal (t ∪ t') = PrimeSpectrum.vanishingIdeal t ⊓ PrimeSpectrum.vanishingIdeal t'- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 68 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites7
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
- Idealstatement · cited by 4,748
- PrimeSpectrumstatement and proof · cited by 625
- GaloisConnection.u_infproof · cited by 37
- PrimeSpectrum.vanishingIdealstatement · cited by 36
- PrimeSpectrum.gcproof · cited by 14
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