Theorems · Definition · field theory

IntermediateField.FG

{F : Type u_1} →
  [inst : Field F] → {E : Type u_2} → [inst_1 : Field E] → [inst_2 : Algebra F E] → IntermediateField F E → Prop

An intermediate field S is finitely generated if there exists t : Finset E such that IntermediateField.adjoin F t = S. We use the class Algebra.EssFiniteType F E instead of (⊤ : IntermediateField F E).FG to say that E is finitely generated as an F extension. See IntermediateField.fg_top_iff.

Defined in

Mathlib.FieldTheory.IntermediateField.Adjoin.Defs

Cited by

17 results in Mathlib

Foundations

Depth 78 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldAlgebra