KnowraAlgebraically closed fieldLinked fromLinked fromThe 8 pages that link to Algebraically closed field, each with the reason it gives.All 8Broader topic 2Related 5Compared with 1Fundamental theorem of algebraRelated: The theorem identifies the complex numbers as an algebraically closed field.Hilbert's NullstellensatzRelated: Algebraic closure ensures the maximal ideals correspond to points over the coefficient field.Schur's lemmaRelated: This hypothesis makes irreducible-representation endomorphisms scalar in the finite-dimensional setting.Lie's theoremRelated: This field condition ensures eigenvalues needed in the common-eigenvector argument exist.Ax–Grothendieck theoremRelated: The theorem's surjectivity conclusion depends on this hypothesis.