liftAlgHom_fieldRange — Mathlib

English

If f lifts g with a composition equality, then f.fieldRange equals the adjoin of g.range.

Русский

Если f восходит g и композиционное равенство выполнено, тогда fieldRange f равняется адъюнкту range g.

LaTeX

$$$f.fieldRange = \operatorname{IntermediateField.adjoin}_F (g.range)$$$

Lean4

/-- The image of `IsFractionRing.liftAlgHom` is the intermediate field generated by the image
of the algebra hom. -/
theorem liftAlgHom_fieldRange (hg : Function.Injective g) :
    (liftAlgHom hg : K →ₐ[F] L).fieldRange = IntermediateField.adjoin F g.range :=
  algHom_fieldRange_eq_of_comp_eq (by ext; simp)

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