Theorems · Theorem · field theory
Normal.minpoly_eq_iff_mem_orbit
∀ {F : Type u_1} [inst : Field F] (E : Type u_6) [inst_1 : Field E] [inst_2 : Algebra F E] [h : Normal F E] {x y : E},
minpoly F x = minpoly F y ↔ x ∈ MulAction.orbit Gal(E/F) y- Defined in
- Mathlib.FieldTheory.Normal.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- AlgHomproof · cited by 3,236
- AlgEquivstatement and proof · cited by 1,681
- minpolystatement and proof · cited by 439
- MulAction.orbitstatement and proof · cited by 114
- Normalstatement and proof · cited by 92
- minpoly.aevalproof · cited by 91
- AlgEquiv.ofBijectiveproof · cited by 34
Cited by1
Results whose statement or proof uses this declaration.
- Polynomial.Gal.galAction_isPretransitiveproof · cited by 0