toIntermediateField — Mathlib

English

The abbreviation toIntermediateField(S) provides the same algebraic-to-intermediate-field construction as in the previous item, via the IsAlgebraic structure on S.

Русский

Сокращение toIntermediateField(S) реализует ту же конструкцию перехода от алгебраической подалгебры к промежуточному полю, используя структуру IsAlgebraic на S.

LaTeX

$$$ \text{toIntermediateField}(S) = (S.isAlgebraic\_iff.mpr\,\langle\_\rangle).toIntermediateField $$$

Lean4

/-- Turn an algebraic subalgebra into an intermediate field, `Algebra.IsAlgebraic` version. -/
abbrev toIntermediateField (S : Subalgebra K L) [Algebra.IsAlgebraic K S] : IntermediateField K L :=
  (S.isAlgebraic_iff.mpr ‹_›).toIntermediateField

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