Theorems · Theorem · algebraic geometry
PrimeSpectrum.le_iff_specializes
∀ {R : Type u} [inst : CommSemiring R] (x y : PrimeSpectrum R), x ≤ y ↔ x ⤳ y- Cited by
- 8 results in Mathlib
- Foundations
- Depth 82 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.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- PrimeSpectrumstatement and proof · cited by 625
- Specializesstatement · cited by 176
- specializes_iff_mem_closureproof · cited by 11
- PrimeSpectrum.le_iff_mem_closureproof · cited by 1
Cited by8
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isClosed_image_of_stableUnderSpecializationproof · cited by 6
- IsLocalRing.specializes_closedPointproof · cited by 6
- Algebra.HasGoingDown.iff_generalizingMap_primeSpectrumComapproof · cited by 4
- PrimeSpectrum.isClosedMap_comap_of_isIntegralproof · cited by 2
- PrimeSpectrum.closure_image_comap_zeroLocusproof · cited by 1
- Algebra.HasGoingUp.iff_specializingMap_primeSpectrumComapproof · cited by 1
- Module.stableUnderSpecialization_supportproof · cited by 0
- PrimeSpectrum.denseRange_comap_iff_minimalPrimesproof · cited by 0