Theorems · Theorem · commutative algebra
Algebra.FormallySmooth.iff_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] (e : A ≃ₐ[R] B), Algebra.FormallySmooth R A ↔ Algebra.FormallySmooth R B- Defined in
- Mathlib.RingTheory.Smooth.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- Algebra.FormallySmoothstatement and proof · cited by 60
- Algebra.FormallySmooth.of_equivproof · cited by 8
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.smoothLocus_eq_univ_iffproof · cited by 3
- Algebra.smoothLocus_comap_of_isLocalizationproof · cited by 1