Theorems · Theorem · field theory
Polynomial.Splits.of_dvd
∀ {R : Type u_1} [inst : CommRing R] {f g : Polynomial R} [IsDomain R], g.Splits → g ≠ 0 → f ∣ g → f.Splits- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 140 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Splitsstatement and proof · cited by 290
- Polynomial.splits_mulproof · cited by 4
Cited by21
Results whose statement or proof uses this declaration.
- IsIntegral.minpoly_splits_tower_top'proof · cited by 3
- FiniteField.nonempty_algHom_of_finrank_dvdproof · cited by 3
- Field.nonempty_algHom_of_exists_rootproof · cited by 3
- Ideal.IsFractionRing.normalproof · cited by 3
- Polynomial.Gal.restrictDvd_defstatement · cited by 2
- Field.primitive_element_inf_auxproof · cited by 1
- gal_X_pow_sub_C_isSolvable_auxproof · cited by 1
- Polynomial.nodup_roots_iff_of_splitsproof · cited by 1
- Polynomial.Gal.restrictDvd_surjectiveproof · cited by 1
- Polynomial.splits_prod_iffproof · cited by 1
- IsAlgClosure.of_splitsproof · cited by 1
- Irreducible.natDegree_dvd_of_dvd_X_pow_card_pow_sub_Xproof · cited by 1