Theorems · Theorem · number theory
FiniteField.splits_X_pow_card_sub_X
∀ (p : ℕ) [h_prime : Fact (Nat.Prime p)] {K : Type u_1} [inst : Field K] [inst_1 : Fintype K]
[inst_2 : Algebra (ZMod p) K],
(Polynomial.map (algebraMap (ZMod p) K) (Polynomial.X ^ Fintype.card K - Polynomial.X)).Splits- Defined in
- Mathlib.FieldTheory.Finite.GaloisField
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Algebrastatement and proof · cited by 11,388
- Fintypestatement and proof · cited by 7,736
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Algebra.algebraMapstatement · cited by 4,706
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Polynomial.Xstatement and proof · cited by 1,639
- Fintype.cardstatement and proof · cited by 1,386
- ZModstatement and proof · cited by 1,024
- Polynomial.mapstatement · cited by 806
- Polynomial.Splitsstatement · cited by 290
Cited by0
Results whose statement or proof uses this declaration.
Nothing cites this yet.