Theorems · Theorem · ring theory
AlgEquiv.injective
∀ {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.Injective ⇑e- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 61 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.
Cites6
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
- EquivLike.injectiveproof · cited by 32
Cited by61
Results whose statement or proof uses this declaration.
- minpoly.algEquiv_eqproof · cited by 13
- AlgEquiv.isAlgebraicproof · cited by 6
- Algebra.FormallyUnramified.isReduced_of_fieldproof · cited by 6
- UpperHalfPlane.gl_smul_eq_iff_num_eqproof · cited by 4
- AlgebraicIndependent.extendScalarsproof · cited by 4
- Algebra.algebraMap_intNormproof · cited by 4
- Algebra.algebraMap_intTraceproof · cited by 4
- AlgEquiv.eq_linearEquivConjAlgEquivproof · cited by 4
- AlgEquiv.isIntegral_iffproof · cited by 3
- PrimeSpectrum.mem_image_comap_basicOpenproof · cited by 3
- IsCyclotomicExtension.equivproof · cited by 3
- ContinuousAlgEquiv.eq_continuousLinearEquivConjContinuousAlgEquivproof · cited by 2