Theorems · Theorem · ring theory
AlgEquiv.bijective
∀ {R : Type uR} {A₁ : Type uA₁} {A₂ : Type uA₂} [inst : CommSemiring R] [inst_1 : Semiring A₁] [inst_2 : Semiring A₂]
[inst_3 : Algebra R A₁] [inst_4 : Algebra R A₂] (e : A₁ ≃ₐ[R] A₂), Function.Bijective ⇑e- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 22 results in Mathlib
- Foundations
- Depth 22 from the axioms · uses 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.
- DFunLike.coestatement · cited by 62,936
- Semiringstatement and proof · cited by 13,802
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- AlgEquivstatement and proof · cited by 1,681
- Function.Bijectivestatement · cited by 863
- EquivLike.bijectiveproof · cited by 15
Cited by22
Results whose statement or proof uses this declaration.
- Algebra.TensorProduct.includeLeft_bijectiveproof · cited by 2
- Ideal.ramificationIdx_smulproof · cited by 2
- IntermediateField.LinearDisjoint.adjoin_rank_eq_rank_left_of_isAlgebraicproof · cited by 2
- TensorProduct.toIntegralClosure_bijective_of_towerproof · cited by 1
- LinearMap.mul'_bijective_of_surjectiveproof · cited by 1
- IsSymmetricAlgebra.of_equivproof · cited by 1
- MvPolynomial.aeval_injective_iff_of_isEmptyproof · cited by 1
- Algebra.IsLocalIso.of_algEquivproof · cited by 1
- IsFractionRing.self_iff_bijectiveproof · cited by 1
- IsLocalization.AtPrime.ramificationIdx_map_eq_ramificationIdxproof · cited by 1