Theorems · Theorem · algebraic geometry
PrimeSpectrum.isClosed_zeroLocus
∀ {R : Type u} [inst : CommSemiring R] (s : Set R), IsClosed (PrimeSpectrum.zeroLocus s)- Cited by
- 10 results in Mathlib
- Foundations
- Depth 79 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.
Cites6
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
- IsClosedstatement · cited by 1,639
- PrimeSpectrumstatement · cited by 625
- PrimeSpectrum.zeroLocusstatement and proof · cited by 164
- PrimeSpectrum.isClosed_iff_zeroLocusproof · cited by 4
Cited by10
Results whose statement or proof uses this declaration.
- PrimeSpectrum.zeroLocus_vanishingIdeal_eq_closureproof · cited by 11
- PrimeSpectrum.isClosed_range_comap_of_surjectiveproof · cited by 2
- PrimeSpectrum.isJacobsonRing_iff_jacobsonSpaceproof · cited by 2
- PrimeSpectrum.isClopen_iffproof · cited by 2
- PrimeSpectrum.closure_image_comap_zeroLocusproof · cited by 1
- PrimeSpectrum.isIntegral_of_isClosedMap_comap_mapRingHomproof · cited by 1
- Localization.exists_finite_awayMapₐ_of_surjective_awayMapₐproof · cited by 1
- PrimeSpectrum.isClopen_basicOpen_of_mul_addproof · cited by 1
- PrimeSpectrum.zeroLocus_ideal_mem_irreducibleComponentsproof · cited by 0
- Module.isClosed_supportproof · cited by 0