Theorems · Theorem · ring theory
AlgEquiv.surjective
∀ {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.Surjective ⇑e- Defined in
- Mathlib.Algebra.Algebra.Equiv
- Cited by
- 48 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.surjectiveproof · cited by 24
Cited by48
Results whose statement or proof uses this declaration.
- Algebra.FinitePresentation.equivproof · cited by 9
- Algebra.QuasiFinite.transproof · cited by 8
- Algebra.FormallySmooth.of_equivproof · cited by 8
- Module.Finite.of_quasiFiniteproof · cited by 7
- Algebra.FormallySmooth.of_comp_surjectiveproof · cited by 6
- Algebra.ZariskisMainProperty.of_finiteType_of_weaklyQuasiFiniteAtproof · cited by 3
- IsCyclotomicExtension.equivproof · cited by 3
- Algebra.FiniteType.equivproof · cited by 3
- KaehlerDifferential.tensorKaehlerEquiv_tmul_Dproof · cited by 3
- IsFractionRing.surjective_iff_isFieldproof · cited by 2
- RingHom.SurjectiveOnStalks.baseChange'proof · cited by 2
- MvPolynomial.comp_C_integral_of_surjective_of_isJacobsonRingproof · cited by 2