Theorems · Theorem · field theory
Polynomial.splits_mul
∀ {R : Type u_1} [inst : CommRing R] {f g : Polynomial R} [IsDomain R],
f ≠ 0 → g ≠ 0 → ((f * g).Splits ↔ f.Splits ∧ g.Splits)- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 139 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Polynomialstatement and proof · cited by 5,681
- mul_commproof · cited by 2,262
- IsDomainstatement and proof · cited by 2,196
- mul_assocproof · cited by 1,667
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- add_commproof · cited by 1,535
- Polynomial.natDegreeproof · cited by 1,105
- Polynomial.evalproof · cited by 796
- Polynomial.Splitsstatement and proof · cited by 290
Cited by4
Results whose statement or proof uses this declaration.
- Polynomial.Splits.of_dvdproof · cited by 21
- Polynomial.Splits.of_natDegree_eq_twoproof · cited by 1
- Polynomial.splits_mul_iffproof · cited by 0
- Normal.of_isSplittingFieldproof · cited by 0