Theorems · Theorem · field theory
IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_pow_of_isSeparable
∀ (F : Type u) (E : Type v) [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] {a : E},
IsSeparable F a → ∀ (q : ℕ) [ExpChar F q] (n : ℕ), F⟮a⟯ = F⟮a ^ q ^ n⟯If F is a field of exponential characteristic q, a : E is separable over F, then
F⟮a⟯ = F⟮a ^ q ^ n⟯ for any natural number n.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 197 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement · cited by 53,352
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- IntermediateFieldstatement · cited by 988
- IntermediateField.adjoinstatement and proof · cited by 382
- ExpCharstatement and proof · cited by 276
- Algebra.IsSeparableproof · cited by 210
- Set.image_singletonproof · cited by 174
- IsSeparablestatement and proof · cited by 68
- IntermediateField.isSeparable_adjoin_simple_iff_isSeparableproof · cited by 4
- IntermediateField.adjoin_eq_adjoin_pow_expChar_pow_of_isSeparableproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- minpoly.iterateFrobenius_of_isSeparableproof · cited by 1
- IntermediateField.adjoin_simple_eq_adjoin_pow_expChar_of_isSeparableproof · cited by 0