Theorems · Theorem · field theory
root_X_pow_sub_C_eq_zero_iff
∀ {K : Type u} [inst : Field K] {n : ℕ} {a : K},
Irreducible (Polynomial.X ^ n - Polynomial.C a) → (AdjoinRoot.root (Polynomial.X ^ n - Polynomial.C a) = 0 ↔ a = 0)- Defined in
- Mathlib.FieldTheory.KummerPolynomial
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 111 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.
Cites18
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
- map_zeroproof · cited by 1,614
- Polynomial.Cstatement and proof · cited by 1,598
- sub_zeroproof · cited by 938
- pow_oneproof · cited by 894
- Irreduciblestatement and proof · cited by 496
- AdjoinRootstatement and proof · cited by 177
- AdjoinRoot.rootstatement and proof · cited by 77
Cited by2
Results whose statement or proof uses this declaration.
- autAdjoinRootXPowSubCEquiv_symm_smulproof · cited by 0
- root_X_pow_sub_C_ne_zero_iffproof · cited by 0