Theorems · Inductive type · field theory
IsAlgClosed
(k : Type u) → [Field k] → Prop
An algebraically closed field is one where every polynomial splits. Equivalently, all
non-constant polynomials have a root. See IsAlgClosed.exists_root and
IsAlgClosed.of_exists_root.
- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 150 results in Mathlib
- Foundations
- Depth 1 from the axioms, rests on 2 definitions · uses no axioms
- Assumes
- Field
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites1
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Fieldstatement · cited by 7,404
Cited by170
Results whose statement or proof uses this declaration.
- IsAlgClosed.splitsstatement and proof · cited by 29
- AlgHom.cardstatement and proof · cited by 10
- Polynomial.natSepDegree_eq_of_isAlgClosedstatement and proof · cited by 9
- IsAlgClosed.exists_rootstatement and proof · cited by 7
- AlgebraicGeometry.residueFieldIsoBasestatement and proof · cited by 6
- IsAlgClosed.algebraMap_bijective_of_isIntegralstatement and proof · cited by 6
- NumberField.Embeddings.cardstatement and proof · cited by 6
- WittVector.RecursionBase.solutionstatement and proof · cited by 6
- AlgebraicGeometry.pointOfClosedPointstatement and proof · cited by 6
- WittVector.frobeniusRotationstatement and proof · cited by 5
- IsAlgClosed.liftstatement and proof · cited by 5
- IsAlgClosed.of_exists_rootstatement · cited by 5