Theorems · Theorem · commutative algebra
RingHom.PropertyIsLocal.HoldsForLocalizationAway
∀ {P : {R S : Type u} → [inst : CommRing R] → [inst_1 : CommRing S] → (R →+* S) → Prop},
RingHom.PropertyIsLocal P →
(RingHom.ContainsIdentities fun {R S} [CommRing R] [CommRing S] => P) → RingHom.HoldsForLocalizationAway P- Defined in
- Mathlib.RingTheory.LocalProperties.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 28 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- RingHom.idproof · cited by 18,349
- CommRingstatement and proof · cited by 17,173
- Algebraproof · cited by 11,388
- RingHomstatement and proof · cited by 10,189
- Algebra.algebraMapproof · cited by 4,706
- RingHom.compproof · cited by 899
- IsLocalization.Awayproof · cited by 218
- RingHomCompTriple.comp_eqproof · cited by 38
- RingHom.PropertyIsLocalstatement and proof · cited by 20
- RingHom.HoldsForLocalizationAwaystatement · cited by 16
- RingHom.ContainsIdentitiesstatement and proof · cited by 12
- RingHom.PropertyIsLocal.StableUnderCompositionWithLocalizationAwayTargetproof · cited by 3
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