Theorems · Theorem · commutative algebra
Algebra.IsStandardEtale.of_surjective
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
[inst_3 : Algebra R S] [inst_4 : Algebra R T] [Algebra.IsStandardEtale R S] [Algebra.Etale R T] (f : S →ₐ[R] T),
Function.Surjective ⇑f → Algebra.IsStandardEtale R TIf T is an etale algebra, and a standard etale algebra surjects onto T, then
T is also standard etale.
- Defined in
- Mathlib.RingTheory.Etale.StandardEtale
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- IsScalarTowerproof · cited by 3,896
- AlgHomstatement and proof · cited by 3,236
- Submodule.spanproof · cited by 1,504
- Ideal.spanproof · cited by 948
- AlgHom.toRingHomproof · cited by 490
- RingHom.kerproof · cited by 363
- RingHom.toAlgebraproof · cited by 337
- IsLocalization.Awayproof · cited by 218
- IsIdempotentElemproof · cited by 217
Cited by1
Results whose statement or proof uses this declaration.
- HasStandardEtaleSurjectionOn.isStandardEtaleproof · cited by 1