Theorems · Theorem · commutative algebra
Algebra.FormallyUnramified.of_surjective
∀ {R : Type u_1} [inst : CommRing R] {A : Type u_2} {B : Type u_3} [inst_1 : CommRing A] [inst_2 : Algebra R A]
[inst_3 : CommRing B] [inst_4 : Algebra R B] [Algebra.FormallyUnramified R A] (f : A →ₐ[R] B),
Function.Surjective ⇑f → Algebra.FormallyUnramified R BThis holds in general for epimorphisms.
- Defined in
- Mathlib.RingTheory.Unramified.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 104 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Idealproof · cited by 4,748
- Bot.botproof · cited by 4,720
- AlgHomstatement and proof · cited by 3,236
- DFunLikeproof · cited by 576
- AlgHom.compproof · cited by 501
- DFunLike.congr_funproof · cited by 288
- AlgHom.extproof · cited by 170
- Ideal.Quotient.mkₐproof · cited by 101
- Algebra.FormallyUnramifiedstatement and proof · cited by 75
Cited by4
Results whose statement or proof uses this declaration.
- RingHom.FormallyUnramified.of_surjectiveproof · cited by 2
- Algebra.FormallyEtale.iff_of_surjectiveproof · cited by 1
- Algebra.FormallyUnramified.pi_iffproof · cited by 1
- Algebra.IsUnramifiedAt.residueFieldproof · cited by 0