Theorems · Definition · ring theory
Algebra.algHom
(R : Type u_1) →
(S : Type u_2) →
(A : Type u_3) →
[inst : CommSemiring R] →
[inst_1 : CommSemiring S] →
[inst_2 : Semiring A] →
[inst_3 : Algebra R S] → [inst_4 : Algebra S A] → [inst_5 : Algebra R A] → [IsScalarTower R S A] → S →ₐ[R] AThe algebra morphism underlying algebraMap.
- Defined in
- Mathlib.Algebra.Algebra.Hom
- Cited by
- 12 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Semiringstatement · cited by 13,802
- Algebrastatement · cited by 11,388
- CommSemiringstatement · cited by 10,911
- IsScalarTowerstatement · cited by 3,896
- AlgHomstatement · cited by 3,236
- IsScalarTower.toAlgHomproof · cited by 232
Cited by17
Results whose statement or proof uses this declaration.
- IntermediateField.extendRightproof · cited by 8
- AdjoinRoot.ofAlgHomproof · cited by 4
- IntermediateField.extendRightEquivproof · cited by 3
- IntermediateField.extendRightEquiv'proof · cited by 3
- IsLocalization.algHom_extstatement and proof · cited by 2
- AdjoinRoot.tensorAlgEquivproof · cited by 2
- TensorProduct.includeRight_lidstatement and proof · cited by 2
- IsArtinianRing.finrank_eq_sum_primeSpectrumproof · cited by 1
- Localization.algHom_extstatement and proof · cited by 1
- TensorProduct.toIntegralClosure_bijective_of_isLocalizationproof · cited by 0
- AdjoinRoot.tensorAlgEquiv_ofproof · cited by 0
- AdjoinRoot.tensorAlgEquiv_rootproof · cited by 0