Commit 2024-11-14 18:07 2ee23a34
View on Github →feat: add some result on IsFractionRing
and fieldRange
(#18984)
In Mathlib/RingTheory/Localization/FractionRing.lean
:
IsFractionRing.closure_range_algebraMap
: ifA
is a ring with fraction fieldK
, then the subfield ofK
generated by the image ofalgebraMap A K
is equal to the whole fieldK
.IsFractionRing.ringHom_fieldRange_eq_of_comp_eq[_of_range_eq]
: ifA
is a ring with fraction fieldK
,L
is a field,g : A →+* L
lifts tof : K →+* L
, then the image off
is the field generated by the image ofg
. InMathlib/FieldTheory/Adjoin.lean
:IsFractionRing.algHom_fieldRange_eq_of_comp_eq[_of_range_eq]
: ifF
is a field,A
is anF
-algebra with fraction fieldK
,L
is a field,g : A →ₐ[F] L
lifts tof : K →ₐ[F] L
,s
is a set such that the image ofg
is the subalgebra generated bys
, then the image off
is the intermediate field generated bys
. Note: this does not requireIsScalarTower F A K
.