Theorems · Theorem · field theory

AlgebraicIndependent.restrictScalars

∀ {ι : Type u} {R : Type u_2} {A : Type v} {x : ι → A} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
  {K : Type u_3} [inst_3 : CommRing K] [inst_4 : Algebra R K] [inst_5 : Algebra K A] [IsScalarTower R K A],
  Function.Injective ⇑(algebraMap R K) → AlgebraicIndependent K x → AlgebraicIndependent R x

A set of algebraically independent elements in an algebra A over a ring K is also algebraically independent over a subring R of K.

Defined in

Mathlib.RingTheory.AlgebraicIndependent.Basic

Cited by

3 results in Mathlib

Foundations

Depth 96 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraCommRingAlgebraAlgebraIsScalarTower