IsAlgClosed.of_exists_root

∀ (k : Type u) [inst : Field k],
  (∀ (p : Polynomial k), p.Monic → Irreducible p → ∃ x, Polynomial.eval x p = 0) → IsAlgClosed k

If every nonconstant polynomial over k has a root, then k is algebraically closed.

Defined in: Mathlib.FieldTheory.IsAlgClosed.Basic
Cited by: 5 results in Mathlib
Foundations: Depth 123 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field

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