Theorems · Theorem · field theory
separableClosure.map_eq_of_algEquiv
∀ {F : Type u} {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {K : Type w} [inst_3 : Field K]
[inst_4 : Algebra F K] (i : E ≃ₐ[F] K), IntermediateField.map (↑i) (separableClosure F E) = separableClosure F KIf i is an F-algebra isomorphism of E and K, then the image of separableClosure F E
under the map i is equal to separableClosure F K.
- Defined in
- Mathlib.FieldTheory.SeparableClosure
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- AlgEquivstatement and proof · cited by 1,681
- IntermediateFieldstatement · cited by 988
- AlgEquiv.symmproof · cited by 615
- LE.le.antisymmproof · cited by 507
- AlgEquiv.toAlgHomstatement and proof · cited by 273
- AlgEquiv.apply_symm_applyproof · cited by 67
- IntermediateField.mapstatement · cited by 62
- separableClosurestatement and proof · cited by 55
- map_mem_separableClosure_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- separableClosure.algEquivOfAlgEquivproof · cited by 0