Theorems · Theorem · algebraic geometry
PrimeSpectrum.localization_comap_injective
∀ {R : Type u} (S : Type v) [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Algebra R S] (M : Submonoid R)
[IsLocalization M S], Function.Injective (PrimeSpectrum.comap (algebraMap R S))- Cited by
- 3 results in Mathlib
- Foundations
- Depth 32 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Idealproof · cited by 4,748
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- Ideal.mapproof · cited by 692
- IsLocalizationstatement and proof · cited by 636
- PrimeSpectrumstatement and proof · cited by 625
- Ideal.comapproof · cited by 443
- PrimeSpectrum.asIdealproof · cited by 333
- PrimeSpectrum.comapstatement and proof · cited by 199
- PrimeSpectrum.extproof · cited by 43
Cited by3
Results whose statement or proof uses this declaration.
- PrimeSpectrum.localization_comap_isEmbeddingproof · cited by 2
- Algebra.QuasiFiniteAt.of_isOpen_singletonproof · cited by 1
- Algebra.exists_etale_isIdempotentElem_forall_liesOver_eqproof · cited by 1