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Theorems · Theorem · commutative algebra

Algebra.FormallySmooth.iff_restrictScalars

∀ {R : Type u} {A : Type v} {B : Type u_1} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
  [inst_3 : CommRing B] [inst_4 : Algebra R B] [inst_5 : Algebra A B] [IsScalarTower R A B] [Algebra.FormallyEtale R A],
  Algebra.FormallySmooth R B ↔ Algebra.FormallySmooth A B
Defined in
Mathlib.RingTheory.Etale.Basic
Cited by
1 results in Mathlib
Foundations
Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTowerAlgebra.FormallyEtale
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

AlgebraicGeometry.formallySmooth_stalkMap_iff · cited by 3AlgebraicGeometry.formall…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraIsScalarTower · cited by 3896IsScalarTowerAlgebra.FormallySmooth · cited by 60Algebra.FormallySmoothAlgebra.FormallyEtale · cited by 37Algebra.FormallyEtaleAlgebra.FormallySmooth.comp · cited by 9FormallySmooth.compAlgebra.FormallySmooth.of_restrictScalars · cited by 2FormallySmooth.of_restric…FormallySmooth.iff_restrictSc…CITED BYCITES

Cites7

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Cited by1

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