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
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- 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
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