Theorems · Theorem · commutative algebra
RingHom.HoldsForLocalization.mk
∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
(RingHom.RespectsIso fun {R S} [CommRing R] [CommRing S] => P) →
(∀ {R : Type u} [inst : CommRing R] (M : Submonoid R), P (algebraMap R (Localization M))) →
RingHom.HoldsForLocalization fun {R S} [CommRing R] [CommRing S] => P- Defined in
- Mathlib.RingTheory.LocalProperties.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 63 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationproof · cited by 636
- AlgEquiv.toAlgHomproof · cited by 273
- Localizationstatement and proof · cited by 270
- RingHom.RespectsIsostatement and proof · cited by 78
- RingEquiv.reflproof · cited by 72
- AlgHom.comp_algebraMapproof · cited by 63
- IsLocalization.algEquivproof · cited by 45
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