Theorems · Theorem · field theory
IsPurelyInseparable.minpoly_eq_X_pow_sub_C
∀ (F : Type u) {E : Type v} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E] (q : ℕ) [ExpChar F q]
[IsPurelyInseparable F E] (x : E), ∃ n y, minpoly F x = Polynomial.X ^ q ^ n - Polynomial.C y- Cited by
- 2 results in Mathlib
- Foundations
- Depth 189 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.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement · cited by 5,681
- Polynomial.Xstatement · cited by 1,639
- Polynomial.Cstatement · cited by 1,598
- minpolystatement · cited by 439
- ExpCharstatement and proof · cited by 276
- IsPurelyInseparablestatement and proof · cited by 84
- isPurelyInseparable_iff_minpoly_eq_X_pow_sub_Cproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- IsPurelyInseparable.minpoly_eqproof · cited by 3
- IsPurelyInseparable.finrank_eq_powproof · cited by 2