Theorems · Theorem · field theory
Polynomial.splits_iff_splits
Deprecated since 2026-01-13Mathlib marks this declaration as deprecated.
∀ {R : Type u_1} [inst : Field R] {f : Polynomial R},
f.Splits ↔ f = 0 ∨ ∀ {g : Polynomial R}, Irreducible g → g ∣ f → g.degree = 1- Defined in
- Mathlib.Algebra.Polynomial.Splits
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Field
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Unitsproof · cited by 2,804
- Units.valproof · cited by 1,966
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- Multiset.prodproof · cited by 528
- Irreduciblestatement and proof · cited by 496
- Polynomial.Splitsstatement and proof · cited by 290
- Units.isUnitproof · cited by 116
- UniqueFactorizationMonoid.factorsproof · cited by 55
- Polynomial.Splits.of_dvdproof · cited by 21
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