Theorems · Theorem · algebraic geometry
PrimeSpectrum.zeroLocus_iUnion
∀ {R : Type u} [inst : CommSemiring R] {ι : Sort u_1} (s : ι → Set R),
PrimeSpectrum.zeroLocus (⋃ i, s i) = ⋂ i, PrimeSpectrum.zeroLocus (s i)- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- Set.iUnionstatement · cited by 2,483
- Set.iInterstatement · cited by 1,084
- PrimeSpectrumstatement · cited by 625
- PrimeSpectrum.zeroLocusstatement · cited by 164
- GaloisConnection.l_iSupproof · cited by 78
- PrimeSpectrum.gc_setproof · cited by 7
Cited by4
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iffproof · cited by 2
- AlgebraicGeometry.Polynomial.isOpenMap_comap_Cproof · cited by 0
- Polynomial.isCompact_image_comap_of_monicproof · cited by 0
- PrimeSpectrum.zeroLocus_bUnionproof · cited by 0