Theorems · Theorem · field theory
root_X_pow_sub_C_ne_zero
∀ {K : Type u} [inst : Field K] {n : ℕ}, 1 < n → ∀ (a : K), AdjoinRoot.root (Polynomial.X ^ n - Polynomial.C a) ≠ 0- Defined in
- Mathlib.FieldTheory.KummerPolynomial
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 109 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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.
- DFunLike.coestatement · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- Polynomial.natDegreeproof · cited by 1,105
- AdjoinRootstatement · cited by 177
- AdjoinRoot.rootstatement · cited by 77
- Polynomial.natDegree_Xproof · cited by 43
- Polynomial.monic_X_pow_sub_Cproof · cited by 13
- Polynomial.X_ne_zeroproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Polynomial.separable_X_pow_sub_C_of_irreducibleproof · cited by 1
- root_X_pow_sub_C_ne_zero'proof · cited by 1