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Theorems · Definition · commutative algebra

IsFractionRing.ringEquivOfRingEquivHom

(A : Type u_8) →
  (K : Type u_9) →
    [inst : CommRing A] → [inst_1 : CommRing K] → [inst_2 : Algebra A K] → [IsFractionRing A K] → (A ≃+* A) →* K ≃+* K

A ring automorphism of a ring induces an ring automorphism of its fraction field. This is a bundled version of ringEquivOfRingEquiv.

Defined in
Mathlib.RingTheory.Localization.FractionRing
Cited by
3 results in Mathlib
Foundations
Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraIsFractionRing
Mathlib docsSourceLoogleLeanSearch

Around this declaration

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

IsFractionRing.mulSemiringAction · cited by 4IsFractionRing.mulSemirin…IsFractionRing.ringEquivOfRingEquivHom.congr_simp · cited by 0ringEquivOfRingEquivHom.c…IsFractionRing.ringEquivOfRingEquivHom_apply · cited by 0IsFractionRing.ringEquivO…IsFractionRing.ringEquivOfRingEquivHom_injective · cited by 0IsFractionRing.ringEquivO…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraMonoidHom · cited by 3629MonoidHomRingEquiv · cited by 1147RingEquivIsFractionRing · cited by 738IsFractionRingIsFractionRing.ringEquivOfRingEquiv · cited by 17IsFractionRing.ringEquivO…IsFractionRing.ringEquivOfRingEquiv_comp · cited by 1IsFractionRing.ringEquivO…IsFractionRing.ringEquivOfRingEquiv_refl · cited by 1IsFractionRing.ringEquivO…IsFractionRing.ringEquivOfRin…CITED BYCITES

Cites8

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by4

Results whose statement or proof uses this declaration.