Theorems · Theorem · field theory
IsGalois.mem_range_algebraMap_iff_fixed
∀ {F : Type u_1} [inst : Field F] {E : Type u_2} [inst_1 : Field E] [inst_2 : Algebra F E] [IsGalois F E]
[FiniteDimensional F E] (x : E), x ∈ Set.range ⇑(algebraMap F E) ↔ ∀ (f : Gal(E/F)), f x = xSee InfiniteGalois.mem_range_algebraMap_iff_fixed for the infinite case,
i.e. without the [FiniteDimensional F E] assumption.
- Defined in
- Mathlib.FieldTheory.Galois.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
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- DFunLike.coestatement · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- Set.rangestatement · cited by 4,705
- FiniteDimensionalstatement and proof · cited by 1,854
- AlgEquivstatement · cited by 1,681
- IsGaloisstatement and proof · cited by 149
- IsGalois.mem_bot_iff_fixedproof · cited by 2
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