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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
Assumes
CommSemiringSemiringSemiringAlgebraAlgebra

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Algebra.FiniteType.isNoetherianRing · cited by 6FiniteType.isNoetherianRi…NumberField.ComplexEmbedding.lift_comp_algebraMap · cited by 3ComplexEmbedding.lift_com…IntermediateField.sepDegree_adjoin_eq_of_isAlgebraic_of_isPurelyInseparable · cited by 2IntermediateField.sepDegr…isIntegral_of_isIntegralElem_of_monic_of_natDegree_lt · cited by 1isIntegral_of_isIntegralE…exists_isIntegral_leadingCoeff_pow_smul_sub_of_isIntegralElem_of_mul_mem_range · cited by 1exists_isIntegral_leading…Polynomial.UniversalCoprimeFactorizationRing.exists_liesOver_residueFieldMap_bijective · cited by 1UniversalCoprimeFactoriza…WeierstrassCurve.Affine.baseChange_nonsingular · cited by 1Affine.baseChange_nonsing…Algebra.IsAlgebraic.normalClosure_le_iSup_adjoin · cited by 1IsAlgebraic.normalClosure…Algebra.WeaklyEtale.ulift_iff · cited by 1WeaklyEtale.ulift_iffAlgebra.exists_notMem_and_isIntegral_forall_mem_of_ne_of_liesOver · cited by 1Algebra.exists_notMem_and…Algebra.WeaklyQuasiFiniteAt.of_algHom_localization · cited by 1WeaklyQuasiFiniteAt.of_al…WeierstrassCurve.Projective.baseChange_equation · cited by 0Projective.baseChange_equ…WeierstrassCurve.Projective.baseChange_nonsingular · cited by 0Projective.baseChange_non…WeierstrassCurve.Affine.Equation.baseChange · cited by 0Equation.baseChangeWeierstrassCurve.Projective.Equation.baseChange · cited by 0Equation.baseChangeSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringRingHom · cited by 10189RingHomAlgHom · cited by 3236AlgHomRingHomClass.toRingHom · cited by 746RingHomClass.toRingHomAlgHom.toRingHom · cited by 490AlgHom.toRingHomAlgHom.toRingHom_eq_coeCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by23

Results whose statement or proof uses this declaration.