Theorems · Theorem · field theory
ne_zero_of_irreducible_X_pow_sub_C
∀ {K : Type u} [inst : Field K] {n : ℕ} {a : K}, Irreducible (Polynomial.X ^ n - Polynomial.C a) → n ≠ 0- Defined in
- Mathlib.FieldTheory.KummerPolynomial
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 104 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.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- pow_zeroproof · cited by 1,094
- map_subproof · cited by 565
- Irreduciblestatement and proof · cited by 496
- RingHom.map_oneproof · cited by 76
- Polynomial.not_irreducible_Cproof · cited by 5
Cited by6
Results whose statement or proof uses this declaration.
- root_X_pow_sub_C_eq_zero_iffproof · cited by 2
- isCyclic_of_isSplittingField_X_pow_sub_Cproof · cited by 1
- autEquivZmod_symm_apply_intCastproof · cited by 1
- Polynomial.separable_X_pow_sub_C_of_irreducibleproof · cited by 1
- finrank_of_isSplittingField_X_pow_sub_Cproof · cited by 0
- isSplittingField_AdjoinRoot_X_pow_sub_Cproof · cited by 0