Theorems · Inductive type · commutative algebra
Algebra.Smooth
(R : Type u_4) → [inst : CommRing R] → (A : Type u) → [inst_1 : CommRing A] → [Algebra R A] → Prop
An R algebra A is smooth if it is formally smooth and of finite presentation.
- Defined in
- Mathlib.RingTheory.Smooth.Basic
- Cited by
- 22 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 by25
Results whose statement or proof uses this declaration.
- RingHom.Smoothproof · cited by 30
- RingHom.etale_iff_formallyUnramified_and_smoothproof · cited by 3
- RingHom.smooth_algebraMapstatement and proof · cited by 3
- Algebra.IsSmoothAt.exists_notMem_isStandardSmoothproof · cited by 2
- Algebra.IsSmoothAt.exists_notMem_smoothstatement · cited by 2
- Algebra.Smooth.exists_subalgebra_fgstatement and proof · cited by 2
- Algebra.Etale.of_formallyUnramified_of_flatproof · cited by 2
- Algebra.Smooth.of_formallySmooth_fiberstatement · cited by 2
- Algebra.Smooth.of_smooth_tensorProduct_of_faithfullyFlatstatement and proof · cited by 2
- Algebra.smooth_iffstatement and proof · cited by 2
- AlgebraicGeometry.exists_smooth_of_formallySmooth_stalkproof · cited by 2
- Algebra.Etale.iff_formallyUnramified_and_smoothstatement and proof · cited by 1