English
For e an AlgEquiv K L L' and E an intermediate field, the image under intermediateFieldMap commutes with the inverse image as a coercion.
Русский
Для AlgEquiv K L L' и промежуточного поля E отображение через intermediateFieldMap взаимодействует с обратной картой как привод к виду.
LaTeX
$$$↑(intermediateFieldMap e E a) = e a\\quad\\text{for } a \\in E.map e.toAlgHom$$$
Lean4
/-- The range of an algebra homomorphism, as an intermediate field. -/
@[simps toSubalgebra]
def fieldRange : IntermediateField K L' :=
{ f.range, (f : L →+* L').fieldRange with }