Theorems · Definition · field theory

IntermediateField.restrictScalars

(K : Type u_1) →
  {L : Type u_2} →
    {L' : Type u_3} →
      [inst : Field K] →
        [inst_1 : Field L] →
          [inst_2 : Field L'] →
            [inst_3 : Algebra K L] →
              [inst_4 : Algebra K L'] →
                [inst_5 : Algebra L' L] → [IsScalarTower K L' L] → IntermediateField L' L → IntermediateField K L

Given a tower L / ↥E / L' / K of field extensions, where E is an L'-intermediate field of L, reinterpret E as a K-intermediate field of L.

Defined in

Mathlib.FieldTheory.IntermediateField.Basic

Cited by

66 results in Mathlib

Foundations

Depth 59 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

FieldFieldFieldAlgebraAlgebraAlgebraIsScalarTower