extendScalars_of_isIntegral — Mathlib

English

If hx is algebraically independent over R and S is integral over R, then hx remains algebraically independent over S.

Русский

Если hx линейно независим над R и S интегрально над R, тогда hx остаётся линейно независимым над S.

LaTeX

$$$$ [Algebra.IsIntegral R S] \Rightarrow \ AlgebraicIndependent R x \to AlgebraicIndependent S x. $$$$

Lean4

theorem extendScalars_of_isIntegral [Algebra.IsIntegral R S] : AlgebraicIndependent S x :=
  by
  nontriviality S
  have := Module.nontrivial R S
  exact hx.extendScalars S

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