Theorems · Definition · number theory
FiniteField.Extension
(k : Type u_1) → [inst : Field k] → (p : ℕ) → [Fact (Nat.Prime p)] → [CharP k p] → ℕ → Type
Given a finite field k of characteristic p, we have a non-canonically chosen extension
of any given degree n > 0.
- Defined in
- Mathlib.FieldTheory.Finite.Extension
- Cited by
- 13 results in Mathlib
- Foundations
- Depth 135 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Factstatement and proof · cited by 2,726
- Nat.Primestatement and proof · cited by 2,059
- Module.finrankproof · cited by 1,770
- ZModproof · cited by 1,024
- CharPstatement and proof · cited by 478
- GaloisFieldproof · cited by 5
Cited by15
Results whose statement or proof uses this declaration.
- FiniteField.Extension.frobstatement and proof · cited by 4
- FiniteField.finrank_extensionstatement and proof · cited by 3
- FiniteField.algEquivExtensionstatement · cited by 3
- FiniteField.finrank_zmod_extensionstatement · cited by 2
- FiniteField.natCard_extensionstatement and proof · cited by 2
- FiniteField.Extension.exists_frob_pow_eqstatement and proof · cited by 1
- FiniteField.Extension.frob_applystatement and proof · cited by 1
- FiniteField.Extension.frob_iterate_applystatement and proof · cited by 1
- Irreducible.natDegree_dvd_of_dvd_X_pow_card_pow_sub_Xproof · cited by 1
- FiniteField.natCard_algEquiv_extensionstatement and proof · cited by 1
- FiniteField.Extension.congr_simpstatement and proof · cited by 0
- FiniteField.algEquivExtension.congr_simpstatement · cited by 0