Theorems · Theorem · field theory
IsSepClosed.roots_eq_zero_iff
∀ {k : Type u} [inst : Field k] [IsSepClosed k] {p : Polynomial k},
p.Separable → (p.roots = 0 ↔ p = Polynomial.C (p.coeff 0))- Defined in
- Mathlib.FieldTheory.IsSepClosed
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 134 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- FieldIsSepClosed
Around this declaration
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Cites19
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Multisetstatement and proof · cited by 2,627
- Polynomial.Cstatement and proof · cited by 1,598
- LT.lt.ne'proof · cited by 1,417
- Polynomial.coeffstatement and proof · cited by 1,045
- Polynomial.degreeproof · cited by 643
- le_or_gtproof · cited by 269
- Polynomial.rootsstatement and proof · cited by 264
- Polynomial.IsRootproof · cited by 152
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