Theorems · Theorem · field theory
isSolvable_gal_minpoly
∀ {F : Type u_1} {E : Type u_2} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {x : E},
x ∈ solvableByRad F E → Group.IsSolvable (minpoly F x).Gal- Defined in
- Mathlib.FieldTheory.AbelRuffini
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- Polynomialproof · cited by 5,681
- IntermediateFieldstatement · cited by 988
- minpolystatement and proof · cited by 439
- AddMemClass.add_memproof · cited by 229
- MulMemClass.mul_memproof · cited by 173
- IntermediateField.subset_adjoinproof · cited by 59
- Group.IsSolvablestatement and proof · cited by 46
- Polynomial.Galstatement and proof · cited by 37
- solvableByRadstatement and proof · cited by 11
- minpoly.eq_X_sub_Cproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- isSolvable_gal_of_irreducibleproof · cited by 1
- solvableByRad.isSolvableproof · cited by 0