Linked from

The 8 pages that link to Algebraically closed field, each with the reason it gives.

• Fundamental theorem of algebraRelated: The theorem identifies the complex numbers as an algebraically closed field.

• Splitting fieldCompared with: Unlike a splitting field for one polynomial, it already splits every polynomial.

• Algebraic closureBroader topic: The closure is itself a field with this defining property.

• 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.

• Quantifier eliminationBroader topic: In this theory, formulas reduce to Boolean combinations of polynomial equations.

• 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.