Theorems · Theorem · field theory
IsAlgClosed.exists_aeval_eq_zero_of_injective
∀ (k : Type u) [inst : Field k] {R : Type u_1} [inst_1 : CommSemiring R] [IsAlgClosed k] [inst_3 : Algebra R k],
Function.Injective ⇑(algebraMap R k) → ∀ (p : Polynomial R), p.degree ≠ 0 → ∃ x, (Polynomial.aeval x) p = 0- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 1 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.
Cites13
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
- Algebrastatement and proof · cited by 11,388
- CommSemiringstatement and proof · cited by 10,911
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · 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
- IsAlgClosedstatement and proof · cited by 150
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgClosed.exists_aeval_eq_zeroproof · cited by 4