Linked from

The 15 pages that link to Splitting field, each with the reason it gives.

• Fundamental theorem of algebraRelated: For complex-coefficient polynomials, the theorem makes the complex field itself sufficient.

• Field extensionBroader topic: It is the minimal extension needed to contain all roots of a polynomial.

• Galois groupRelated: Its automorphisms permute all roots while preserving their algebraic relations.

• Évariste GaloisRelated: It contains all the roots whose symmetries form the equation's Galois group.

• Cyclotomic fieldNarrower topic: A cyclotomic field is the splitting field of a cyclotomic polynomial.

• Galois theoryRelated: Automorphisms of this field capture the polynomial's root symmetries.

• Algebraic closureRelated: Splitting fields supply the roots of individual polynomials before considering all polynomials at once.

• FieldBroader topic: It constructs the specific extension needed to contain all roots of a polynomial.

• Algebraically closed fieldRelated: A closed field contains a splitting field for every polynomial over its subfields.

• Field automorphismRelated: Automorphisms of a splitting field permute the polynomial’s roots while preserving their relations.

• Inverse Galois problemRelated: A polynomial’s splitting field is a standard source of Galois extensions.

• Solvability by radicalsRelated: The Galois group used in the criterion acts on the polynomial’s splitting field.

• Normal extensionRelated: A normal extension is a splitting field for a suitable family of base-field polynomials.

• Primitive element theoremRelated: Distinct roots in splitting fields are central to defining separability.

• Schinzel's theoremRelated: Its Galois group provides a framework for understanding primes where a polynomial has roots.