Theorems · Definition · ring theory
RingEquiv.toRatAlgEquiv
{R : Type u_1} →
{S : Type u_2} →
[inst : Ring R] → [inst_1 : Ring S] → [inst_2 : Algebra ℚ R] → [inst_3 : Algebra ℚ S] → R ≃+* S → R ≃ₐ[ℚ] SReinterpret a RingEquiv as a ℚ-algebra isomorphism. This actually yields an
equivalence, see RingEquiv.equivRatAlgEquiv.
- Defined in
- Mathlib.Algebra.Algebra.Hom.Rat
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 87 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Equivproof · cited by 8,337
- Ringstatement and proof · cited by 7,463
- AlgHomproof · cited by 3,236
- AlgEquivstatement · cited by 1,681
- RingEquivstatement and proof · cited by 1,147
- RingEquiv.toRingHomproof · cited by 150
- EquivLike.toEquivproof · cited by 125
- RingHom.toRatAlgHomproof · cited by 11
Cited by9
Results whose statement or proof uses this declaration.
- RingEquiv.equivRatAlgEquivproof · cited by 3
- RingEquiv.equivRatAlgEquiv_applystatement · cited by 0
- RingEquiv.toAlgHom_toRatAlgEquivstatement · cited by 0
- AlgEquiv.toRatAlgEquiv_toRingEquivstatement · cited by 0
- RingEquiv.toRatAlgEquiv_applystatement and proof · cited by 0
- RingEquiv.toRatAlgEquiv_injectivestatement · cited by 0
- RingEquiv.toRingEquiv_toRatAlgEquivstatement · cited by 0
- RingEquiv.coe_toRatAlgEquivstatement · cited by 0
- RingEquiv.symm_toRatAlgEquivstatement · cited by 0