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: ifAis a ring with fraction fieldK, then the subfield ofKgenerated by the image ofalgebraMap A Kis equal to the whole fieldK.IsFractionRing.ringHom_fieldRange_eq_of_comp_eq[_of_range_eq]: ifAis a ring with fraction fieldK,Lis a field,g : A →+* Llifts tof : K →+* L, then the image offis the field generated by the image ofg. InMathlib/FieldTheory/Adjoin.lean:IsFractionRing.algHom_fieldRange_eq_of_comp_eq[_of_range_eq]: ifFis a field,Ais anF-algebra with fraction fieldK,Lis a field,g : A →ₐ[F] Llifts tof : K →ₐ[F] L,sis a set such that the image ofgis the subalgebra generated bys, then the image offis the intermediate field generated bys. Note: this does not requireIsScalarTower F A K.