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Theorems · Theorem · algebraic geometry

PrimeSpectrum.zeroLocus_inf

∀ {R : Type u} [inst : CommSemiring R] (I J : Ideal R),
  PrimeSpectrum.zeroLocus ↑(I ⊓ J) = PrimeSpectrum.zeroLocus ↑I ∪ PrimeSpectrum.zeroLocus ↑J
Defined in
Mathlib.RingTheory.Spectrum.Prime.Basic
Cited by
2 results in Mathlib
Foundations
Depth 73 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiring
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.Scheme.zeroLocus_inf · cited by 0Scheme.zeroLocus_infPrimeSpectrum.union_zeroLocus · cited by 0PrimeSpectrum.union_zeroL…Set · cited by 53352SetCommSemiring · cited by 10911CommSemiringSetLike.coe · cited by 8199SetLike.coeIdeal · cited by 4748IdealSet.ext · cited by 2266Set.extPrimeSpectrum · cited by 625PrimeSpectrumPrimeSpectrum.zeroLocus · cited by 164PrimeSpectrum.zeroLocusIdeal.IsPrime.inf_le · cited by 3IsPrime.inf_lePrimeSpectrum.zeroLocus_infCITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.