KnowraAlgebraic closureLinked fromLinked fromThe 14 pages that link to Algebraic closure, each with the reason it gives.All 14Broader topic 1Related 6Narrower topic 5Compared with 2Discriminant (polynomial)Related: Repeated-root detection is understood over an algebraic closure, even when roots are not in the coefficient field.FieldRelated: Every field has an algebraic closure in which all nonconstant polynomials split.Frobenius endomorphismRelated: Frobenius behavior on algebraic closures helps describe purely inseparable extensions.Solvability by radicalsRelated: It supplies a common setting in which all polynomial roots and their radical expressions can be considered.Jordan–Chevalley decompositionRelated: Diagonalizability and Jordan blocks are often described after extending scalars to such a field.Gelfand–Mazur theoremRelated: The theorem depends on the complex field’s algebraic closure through spectral theory.