Theorems · Theorem · algebraic geometry
PrimeSpectrum.ext
∀ {R : Type u_1} {inst : CommSemiring R} {x y : PrimeSpectrum R}, x.asIdeal = y.asIdeal → x = y- Defined in
- Mathlib.RingTheory.Spectrum.Prime.Defs
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses no axioms
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
- Idealstatement and proof · cited by 4,748
- Ideal.IsPrimeproof · cited by 827
- PrimeSpectrumstatement and proof · cited by 625
- PrimeSpectrum.asIdealstatement and proof · cited by 333
Cited by43
Results whose statement or proof uses this declaration.
- PrimeSpectrum.isClosed_singleton_iff_isMaximalproof · cited by 8
- PrimeSpectrum.ext_iffproof · cited by 7
- PrimeSpectrum.comap_injective_of_surjectiveproof · cited by 5
- Algebra.HasGoingDown.iff_generalizingMap_primeSpectrumComapproof · cited by 4
- AlgebraicGeometry.ProjectiveSpectrum.Proj.toSpec_base_apply_eqproof · cited by 3
- PrimeSpectrum.localization_comap_injectiveproof · cited by 3
- PrimeSpectrum.exists_comap_evalRingHom_eqproof · cited by 3
- PrimeSpectrum.comap_evalRingHom_basicOpenproof · cited by 2
- PrimeSpectrum.localization_comap_rangeproof · cited by 2
- Algebra.QuasiFiniteAt.exists_basicOpen_eq_singletonproof · cited by 2
- PrimeSpectrum.mem_image_comap_zeroLocus_sdiffproof · cited by 2
- PrimeSpectrum.exists_multiset_prod_cons_le_and_prod_not_leproof · cited by 2