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Theorems · Theorem · commutative algebra

IsFractionRing.ringEquivOfRingEquiv_algebraMap

∀ {A : Type u_8} {K : Type u_9} {B : Type u_10} {L : Type u_11} [inst : CommRing A] [inst_1 : CommRing B]
  [inst_2 : CommRing K] [inst_3 : CommRing L] [inst_4 : Algebra A K] [inst_5 : IsFractionRing A K]
  [inst_6 : Algebra B L] [inst_7 : IsFractionRing B L] (h : A ≃+* B) (a : A),
  (IsFractionRing.ringEquivOfRingEquiv h) ((algebraMap A K) a) = (algebraMap B L) (h a)
Defined in
Mathlib.RingTheory.Localization.FractionRing
Cited by
2 results in Mathlib
Foundations
Depth 61 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingCommRingCommRingAlgebraIsFractionRingAlgebraIsFractionRing
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

IsFractionRing.fieldEquivOfAlgEquiv_algebraMap · cited by 4IsFractionRing.fieldEquiv…IsFractional.mapEquiv · cited by 2IsFractional.mapEquivDFunLike.coe · cited by 62936DFunLike.coeCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraRingHom · cited by 10189RingHomAlgebra.algebraMap · cited by 4706Algebra.algebraMapRingEquiv · cited by 1147RingEquivIsFractionRing · cited by 738IsFractionRingIsLocalization.map_eq · cited by 34IsLocalization.map_eqIsFractionRing.ringEquivOfRingEquiv · cited by 17IsFractionRing.ringEquivO…IsFractionRing.ringEquivOfRingEquiv_apply · cited by 7IsFractionRing.ringEquivO…IsFractionRing.ringEquivOfRin…CITED BYCITES

Cites10

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Cited by2

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