Theorems · Definition · ring theory
RingHom.equivRatAlgHom
(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] S)The equivalence between RingHom and ℚ-algebra homomorphisms.
- 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.
Cites7
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
- RingHomstatement · cited by 10,189
- Equivstatement · cited by 8,337
- Ringstatement and proof · cited by 7,463
- AlgHomstatement · cited by 3,236
- AlgHom.toRingHomproof · cited by 490
- RingHom.toRatAlgHomproof · cited by 11
Cited by8
Results whose statement or proof uses this declaration.
- NumberField.InfinitePlace.prod_eq_abs_normproof · cited by 8
- NumberField.Embeddings.cardproof · cited by 6
- NumberField.mixedEmbedding.volume_fundamentalDomain_latticeBasisproof · cited by 4
- NumberField.basisMatrix_eq_embeddingsMatrixReindexstatement · cited by 2
- RingHom.equivRatAlgHom_applystatement and proof · cited by 2
- NumberField.det_of_basisMatrix_non_zeroproof · cited by 1
- NumberField.discr_eq_basisMatrix_det_sqproof · cited by 1
- RingHom.equivRatAlgHom_symm_applystatement and proof · cited by 0