Theorems · Theorem · field theory
X_pow_sub_C_irreducible_iff_of_prime_pow
∀ {K : Type u} [inst : Field K] {p : ℕ},
Nat.Prime p →
p ≠ 2 → ∀ {n : ℕ}, n ≠ 0 → ∀ {a : K}, Irreducible (Polynomial.X ^ p ^ n - Polynomial.C a) ↔ ∀ (b : K), b ^ p ≠ a- Defined in
- Mathlib.FieldTheory.KummerExtension
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 138 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites13
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 · cited by 5,681
- Nat.Primestatement and proof · cited by 2,059
- Polynomial.Xstatement and proof · cited by 1,639
- Polynomial.Cstatement and proof · cited by 1,598
- Irreduciblestatement and proof · cited by 496
- dvd_rflproof · cited by 80
- Nat.Prime.ne_oneproof · cited by 61
- dvd_powproof · cited by 8
- pow_ne_of_irreducible_X_pow_sub_Cproof · cited by 4
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