Theorems · Theorem · field theory
Polynomial.Separable.of_dvd
∀ {R : Type u} [inst : CommSemiring R] {f g : Polynomial R}, f.Separable → g ∣ f → g.Separable- Defined in
- Mathlib.FieldTheory.Separable
- Cited by
- 14 results in Mathlib
- Foundations
- Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommSemiring
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- Polynomial.Separablestatement and proof · cited by 117
- Polynomial.Separable.of_mul_leftproof · cited by 4
Cited by14
Results whose statement or proof uses this declaration.
- IsSeparable.tower_topproof · cited by 11
- isPurelyInseparable_iff_pow_memproof · cited by 10
- IsSeparable.of_algebra_isSeparable_of_isSeparableproof · cited by 3
- isSeparable_algebraMapproof · cited by 3
- IsCyclotomicExtension.isSeparableproof · cited by 3
- Algebra.IsAlgebraic.perfectFieldproof · cited by 2
- Polynomial.separable_cyclotomicproof · cited by 2
- IsPrimitiveRoot.separable_minpoly_modproof · cited by 2
- IsSepClosed.separableClosure_eq_bot_iffproof · cited by 1
- Polynomial.separable_gcd_rightproof · cited by 1
- IsSepClosed.of_exists_rootproof · cited by 1
- IsGalois.of_separable_splitting_field_auxproof · cited by 0