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Theorems · Theorem · commutative algebra

RingHom.localization_away_map_finite

∀ (R S R' S' : Type u) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing R'] [inst_3 : CommRing S']
  [inst_4 : Algebra R R'] (f : R →+* S) [inst_5 : Algebra S S'] (r : R) [inst_6 : IsLocalization.Away r R']
  [inst_7 : IsLocalization.Away (f r) S'], f.Finite → (IsLocalization.Away.map R' S' f r).Finite
Defined in
Mathlib.RingTheory.RingHom.Finite
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0 results in Mathlib
Foundations
Depth 79 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingCommRingCommRingAlgebraAlgebraIsLocalization.AwayIsLocalization.Away
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DFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRingHom · cited by 10189RingHomIsLocalization.Away · cited by 218IsLocalization.AwayRingHom.Finite · cited by 48RingHom.FiniteIsLocalization.Away.map · cited by 19Away.mapRingHom.LocalizationPreserves.away · cited by 9LocalizationPreserves.awayRingHom.finite_localizationPreserves · cited by 1RingHom.finite_localizati…RingHom.localization_away_map…CITED BYCITES

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