Theorems · Theorem · ring theory
AlgHom.toRingHom_eq_coe
∀ {R : Type u} {A : Type v} {B : Type w} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Semiring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] (f : A →ₐ[R] B), f.toRingHom = ↑f- Defined in
- Mathlib.Algebra.Algebra.Hom
- Cited by
- 23 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses no axioms
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.
- 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
- AlgHomstatement and proof · cited by 3,236
- RingHomClass.toRingHomstatement · cited by 746
- AlgHom.toRingHomstatement · cited by 490
Cited by23
Results whose statement or proof uses this declaration.
- Algebra.FiniteType.isNoetherianRingproof · cited by 6
- NumberField.ComplexEmbedding.lift_comp_algebraMapproof · cited by 3
- isIntegral_of_isIntegralElem_of_monic_of_natDegree_ltproof · cited by 1
- WeierstrassCurve.Affine.baseChange_nonsingularproof · cited by 1
- Algebra.IsAlgebraic.normalClosure_le_iSup_adjoinproof · cited by 1
- Algebra.WeaklyEtale.ulift_iffproof · cited by 1
- Algebra.exists_notMem_and_isIntegral_forall_mem_of_ne_of_liesOverproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.of_algHom_localizationproof · cited by 1
- WeierstrassCurve.Projective.baseChange_equationproof · cited by 0