Theorems · Theorem · algebraic geometry
PrimeSpectrum.zeroLocus_span
∀ {R : Type u} [inst : CommSemiring R] (s : Set R), PrimeSpectrum.zeroLocus ↑(Ideal.span s) = PrimeSpectrum.zeroLocus s- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Basic
- Cited by
- 17 results in Mathlib
- Foundations
- Depth 62 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.
Cites11
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 · cited by 8,199
- Idealstatement · cited by 4,748
- Set.extproof · cited by 2,266
- Ideal.spanstatement · cited by 948
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealproof · cited by 333
- PrimeSpectrum.zeroLocusstatement · cited by 164
- GaloisInsertion.gcproof · cited by 137
- Submodule.giproof · cited by 12
Cited by17
Results whose statement or proof uses this declaration.
- PrimeSpectrum.gc_setproof · cited by 7
- PrimeSpectrum.iSup_basicOpen_eq_top_iffproof · cited by 6
- PrimeSpectrum.isClosed_iff_zeroLocus_idealproof · cited by 4
- ringKrullDim_quotient_succ_le_of_nonZeroDivisorproof · cited by 3
- AlgebraicGeometry.IsAffineOpen.iSup_basicOpen_eq_self_iffproof · cited by 2
- Module.support_quotSMulTopproof · cited by 2
- PrimeSpectrum.isIntegral_of_isClosedMap_comap_mapRingHomproof · cited by 1
- PrimeSpectrum.isRetrocompact_zeroLocus_compl_of_fgproof · cited by 1
- PrimeSpectrum.localization_comap_isInducingproof · cited by 1
- PrimeSpectrum.isCompact_isOpen_iff_idealproof · cited by 1
- AlgebraicGeometry.eq_top_of_sigmaSpec_subset_of_isCompactproof · cited by 1
- PrimeSpectrum.zeroLocus_subset_zeroLocus_singleton_iffproof · cited by 1