Mathlib Map

Theorems · Theorem · number theory

FiniteField.isSplittingField_of_nat_card_eq

∀ (p : ℕ) [h_prime : Fact (Nat.Prime p)] (n : ℕ) {K : Type u_1} [inst : Field K] [inst_1 : Algebra (ZMod p) K],
  Nat.card K = p ^ n → Polynomial.IsSplittingField (ZMod p) K (Polynomial.X ^ p ^ n - Polynomial.X)
Defined in
Mathlib.FieldTheory.Finite.GaloisField
Cited by
0 results in Mathlib
Foundations
Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FactFieldAlgebra

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites17

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
  • Fintypeproof · cited by 7,736
  • Fieldstatement and proof · cited by 7,404
  • Polynomialstatement · cited by 5,681
  • Finiteproof · cited by 3,029
  • Factstatement and proof · cited by 2,726
  • Nat.Primestatement and proof · cited by 2,059
  • Polynomial.Xstatement and proof · cited by 1,639
  • ZModstatement and proof · cited by 1,024
  • Nat.cardstatement and proof · cited by 844
  • Fact.outproof · cited by 328
  • pow_posproof · cited by 292

Cited by0

Results whose statement or proof uses this declaration.

Nothing cites this yet.