Theorems · Theorem · ring theory
AlgEquiv.commutes
∀ {R : Type uR} {A₁ : Type uA₁} {A₂ : Type uA₂} [inst : CommSemiring R] [inst_1 : Semiring A₁] [inst_2 : Semiring A₂]
[inst_3 : Algebra R A₁] [inst_4 : Algebra R A₂] (e : A₁ ≃ₐ[R] A₂) (r : R),
e ((algebraMap R A₁) r) = (algebraMap R A₂) r- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 49 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement · cited by 4,706
- AlgEquivstatement and proof · cited by 1,681
- AlgEquiv.commutes'proof · cited by 4
Cited by49
Results whose statement or proof uses this declaration.
- IsLocalization.isLocalization_of_algEquivproof · cited by 11
- RingHom.CodescendsAlong.mkproof · cited by 8
- AlgebraicGeometry.basicOpen_eq_of_affineproof · cited by 5
- IntermediateField.fixingSubgroup_botproof · cited by 4
- Algebra.algebraMap_intNormproof · cited by 4
- Algebra.algebraMap_intTraceproof · cited by 4
- AlgebraicGeometry.localRingHom_comp_stalkIsoproof · cited by 3
- PrimeSpectrum.mem_image_comap_basicOpenproof · cited by 3
- AlgebraicGeometry.stalkClosedPointIso_invproof · cited by 3
- Ideal.inertiaDeg_eq_of_isFractionRingproof · cited by 2
- Algebra.IsStandardEtale.of_isLocalizationAwayproof · cited by 2
- NumberField.ComplexEmbedding.IsConj.isReal_compproof · cited by 2