Theorems · Theorem · field theory
AlgHom.fieldRange_le_normalClosure
∀ {F : Type u_1} {K : Type u_2} {L : Type u_3} [inst : Field F] [inst_1 : Field K] [inst_2 : Field L]
[inst_3 : Algebra F K] [inst_4 : Algebra F L] (f : K →ₐ[F] L), f.fieldRange ≤ IntermediateField.normalClosure F K L- Defined in
- Mathlib.FieldTheory.Normal.Closure
- Cited by
- 3 results in Mathlib
- Foundations
- Depth 86 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- AlgHomstatement and proof · cited by 3,236
- IntermediateFieldstatement · cited by 988
- le_iSupproof · cited by 207
- AlgHom.fieldRangestatement and proof · cited by 57
- IntermediateField.normalClosurestatement · cited by 38
Cited by3
Results whose statement or proof uses this declaration.
- IntermediateField.le_normalClosureproof · cited by 8
- IntermediateField.finrank_eq_fixingSubgroup_indexproof · cited by 1
- Algebra.IsAlgebraic.isNormalClosure_normalClosureproof · cited by 0