Theorems · Theorem · field theory
IsAlgClosed.exists_aeval_eq_zero
∀ (k : Type u) [inst : Field k] {R : Type u_1} [inst_1 : CommSemiring R] [IsAlgClosed k] [inst_3 : Algebra R k]
[FaithfulSMul R k] (p : Polynomial R), p.degree ≠ 0 → ∃ x, (Polynomial.aeval x) p = 0- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 117 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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
- 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
- IsAlgClosedstatement and proof · cited by 150
Cited by4
Results whose statement or proof uses this declaration.
- Irreducible.natDegree_le_twoproof · cited by 2
- Polynomial.natSepDegree_mul_eq_iffproof · cited by 1
- Polynomial.Separable.map_irreducible_of_isPurelyInseparableproof · cited by 0
- IsAlgClosed.algebraicClosure_eq_bot_iffproof · cited by 0