Theorems · Theorem · algebraic geometry
PrimeSpectrum.sup_vanishingIdeal_le
∀ {R : Type u} [inst : CommSemiring R] (t t' : Set (PrimeSpectrum R)),
PrimeSpectrum.vanishingIdeal t ⊔ PrimeSpectrum.vanishingIdeal t' ≤ PrimeSpectrum.vanishingIdeal (t ∩ t')- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 76 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
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Cites9
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
- PrimeSpectrum.asIdealproof · cited by 333
- Submodule.add_memproof · cited by 75
- Submodule.mem_supproof · cited by 73
- PrimeSpectrum.vanishingIdealstatement and proof · cited by 36
- PrimeSpectrum.mem_vanishingIdealproof · cited by 4
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