intermediateField — Mathlib

English

The intermediate field fixed by a monoid action that commutes with the F-action on E is given by the fixed points of that action.

Русский

Промежуточное поле фиксированных точек действия моноида, коммутирующее с действием F на E, состоит из фиксаций этого действия.

LaTeX

$$IntermediateField {F} E = FixedPoints.subfield M E$$

Lean4

/-- The intermediate field of fixed points fixed by a monoid action that commutes with the
`F`-action on `E`. -/
def intermediateField (M : Type*) [Monoid M] [MulSemiringAction M E] [SMulCommClass M F E] : IntermediateField F E :=
  { FixedPoints.subfield M E with
    carrier := MulAction.fixedPoints M E
    algebraMap_mem' := fun a g => smul_algebraMap g a }

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