Theorems · Theorem · commutative algebra
Algebra.FormallySmooth.of_equiv
∀ {R : Type u_4} [inst : CommRing R] {A : Type u_5} {B : Type u_6} [inst_1 : CommRing A] [inst_2 : Algebra R A]
[inst_3 : CommRing B] [inst_4 : Algebra R B] [Algebra.FormallySmooth R A] (e : A ≃ₐ[R] B), Algebra.FormallySmooth R B- Defined in
- Mathlib.RingTheory.Smooth.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- AlgEquivstatement and proof · cited by 1,681
- AlgEquiv.symmproof · cited by 615
- AlgHom.compproof · cited by 501
- AlgHom.toRingHomproof · cited by 490
- RingHom.kerproof · cited by 363
- AlgEquiv.toAlgHomproof · cited by 273
- AlgHom.extproof · cited by 170
- Ideal.Quotient.mkₐproof · cited by 101
- AlgEquiv.apply_symm_applyproof · cited by 67
- Algebra.FormallySmoothstatement and proof · cited by 60
Cited by8
Results whose statement or proof uses this declaration.
- Algebra.FormallyEtale.of_equivproof · cited by 3
- Algebra.Smooth.of_smooth_tensorProduct_of_faithfullyFlatproof · cited by 2
- Algebra.FormallySmooth.adjoin_of_algebraicIndependentproof · cited by 2
- Algebra.FormallySmooth.iff_of_equivproof · cited by 2
- Algebra.IsSmoothAt.of_formallySmooth_fiberproof · cited by 1
- RingHom.FormallySmooth.of_bijectiveproof · cited by 1
- Algebra.Smooth.of_equivproof · cited by 0
- Algebra.FormallySmooth.of_algebraicIndependentproof · cited by 0