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Theorems · Definition · ring theory

AlgEquiv.toMulEquiv

{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] → (A ≃ₐ[R] B) → A ≃* B
Defined in
Mathlib.Algebra.Algebra.Equiv
Cited by
13 results in Mathlib
Foundations
Depth 13 from the axioms · uses no axioms
Assumes
CommSemiringSemiringSemiringAlgebraAlgebra

Around this declaration

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

IsIntegralClosure.isLocalization · cited by 13IsIntegralClosure.isLocal…Matrix.GeneralLinearGroup.toLin · cited by 4GeneralLinearGroup.toLinIsBaseChange.lift_rank_eq · cited by 3IsBaseChange.lift_rank_eqAlgebra.TensorProduct.isField_of_isAlgebraic · cited by 2TensorProduct.isField_of_…exists_isTranscendenceBasis_and_isSeparable_of_linearIndepOn_pow · cited by 2exists_isTranscendenceBas…IntermediateField.LinearDisjoint.of_isField · cited by 1LinearDisjoint.of_isFieldTranscendental.uniqueFactorizationMonoid_adjoin · cited by 1Transcendental.uniqueFact…IntermediateField.LinearDisjoint.isDomain · cited by 1LinearDisjoint.isDomainAddChar.FiniteField.primitiveChar_to_Complex · cited by 1FiniteField.primitiveChar…Subalgebra.LinearDisjoint.isDomain_of_injective · cited by 1LinearDisjoint.isDomain_o…IntermediateField.LinearDisjoint.of_isField' · cited by 0LinearDisjoint.of_isField'Ideal.exists_comap_galRestrict_eq · cited by 0Ideal.exists_comap_galRes…IntermediateField.LinearDisjoint.algEquiv_of_isAlgebraic · cited by 0LinearDisjoint.algEquiv_o…Subalgebra.LinearDisjoint.of_isField' · cited by 0LinearDisjoint.of_isField'Ideal.IsField.of_isPrincipalIdealRing_polynomial · cited by 0IsField.of_isPrincipalIde…Semiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringAlgEquiv · cited by 1681AlgEquivMulEquiv · cited by 1142MulEquivAlgEquiv.toEquiv · cited by 65AlgEquiv.toEquivAlgEquiv.map_mul' · cited by 19AlgEquiv.map_mul'AlgEquiv.toMulEquivCITED BYCITES

Cites7

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

Cited by15

Results whose statement or proof uses this declaration.