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Theorems · Theorem · commutative algebra

Algebra.Smooth.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.Smooth R A] (e : A ≃ₐ[R] B), Algebra.Smooth R B

Being smooth is transported via algebra isomorphisms.

Defined in
Mathlib.RingTheory.Smooth.Basic
Cited by
0 results in Mathlib
Foundations
Depth 130 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraCommRingAlgebraAlgebra.Smooth
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CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraAlgEquiv · cited by 1681AlgEquivAlgebra.Smooth · cited by 22Algebra.SmoothAlgebra.FinitePresentation.equiv · cited by 9FinitePresentation.equivAlgebra.FormallySmooth.of_equiv · cited by 8FormallySmooth.of_equivSmooth.of_equivCITED BYCITES

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