Theorems · Theorem · field theory
root_X_pow_sub_C_ne_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
- 0 results in Mathlib
- Foundations
- Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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- DFunLike.coestatement and proof · 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 and proof · cited by 1,598
- Irreduciblestatement and proof · cited by 496
- Iff.notproof · cited by 489
- AdjoinRootstatement · cited by 177
- AdjoinRoot.rootstatement · cited by 77
- root_X_pow_sub_C_eq_zero_iffproof · cited by 2
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