Theorems · Inductive type · commutative algebra
Algebra.Etale
(R : Type u) → (A : Type v) → [inst : CommRing R] → [inst_1 : CommRing A] → [Algebra R A] → Prop
An R-algebra A is étale if it is formally étale and of finite presentation.
- Defined in
- Mathlib.RingTheory.Etale.Basic
- Cited by
- 34 results in Mathlib
- Foundations
- Depth 6 from the axioms · uses no axioms
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites2
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
Cited by40
Results whose statement or proof uses this declaration.
- RingHom.Etaleproof · cited by 26
- CommAlgCat.FiniteEtale.ofstatement and proof · cited by 6
- RingHom.etale_algebraMapstatement and proof · cited by 3
- RingHom.etale_iff_formallyUnramified_and_smoothproof · cited by 3
- CommAlgCat.FiniteEtale.ofHomstatement and proof · cited by 2
- Algebra.Etale.iff_isStandardSmoothOfRelativeDimension_zerostatement and proof · cited by 2
- Algebra.Etale.of_formallyUnramified_of_flatstatement · cited by 2
- Algebra.IsEtaleAt.exists_isStandardEtaleproof · cited by 1
- IsLocalRing.finrank_eq_finrank_residueFieldstatement and proof · cited by 1
- Algebra.IsStandardEtale.of_surjectivestatement and proof · cited by 1
- Algebra.etale_iffstatement and proof · cited by 1
- Algebra.exists_etale_bijective_residueFieldMap_and_map_eq_mul_and_isCoprimestatement · cited by 1