Theorems · Theorem · field theory
IsSepClosed.exists_aeval_eq_zero
∀ (K : Type v) [inst : Field K] {k : Type u_1} [inst_1 : CommSemiring k] [IsSepClosed K] [inst_3 : Algebra k K]
[FaithfulSMul k K] (p : Polynomial k), p.degree ≠ 0 → p.Separable → ∃ x, (Polynomial.aeval x) p = 0- Defined in
- Mathlib.FieldTheory.IsSepClosed
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement · cited by 3,236
- WithBotstatement · cited by 1,498
- Polynomial.degreestatement and proof · cited by 643
- Polynomial.aevalstatement · cited by 615
- FaithfulSMulstatement and proof · cited by 340
- FaithfulSMul.algebraMap_injectiveproof · cited by 198
Cited by2
Results whose statement or proof uses this declaration.
- IsSepClosed.separableClosure_eq_bot_iffproof · cited by 1
- IsSepClosed.isCyclotomicExtensionproof · cited by 0