KnowraField extensionLinked fromLinked fromThe 29 pages that link to Field extension, each with the reason it gives.All 29Related 15Narrower topic 14Field (mathematics)Related: Extensions enlarge a field while preserving its arithmetic operations.Évariste GaloisRelated: Adjoining polynomial roots creates the extensions whose symmetries Galois theory studies.FieldRelated: Extensions describe how fields acquire solutions to additional polynomial equations.Angle trisectionRelated: Constructible lengths arise through restricted sequences of quadratic field extensions.Doubling the cubeRelated: Compass-and-straightedge constructions produce numbers through extensions of degree a power of two.Lindemann–Weierstrass theoremRelated: Algebraic numbers form a field extension of the rationals, where the theorem's coefficients lie.Squaring the circleRelated: Constructible lengths arise through field extensions of degree that is a power of two.Straightedge and compass constructionRelated: Constructible coordinates arise through successive quadratic field extensions.Algebraically closed fieldRelated: Roots missing from a field can be added by passing to an extension.Field automorphismRelated: Automorphisms often become significant when they fix a base field inside an extension.Hyperreal numberRelated: The hyperreals extend the real field without changing its embedded elements.Jordan–Chevalley decompositionRelated: The meaning of semisimple can depend on whether diagonalizability is tested over the base field or an extension.Noether normalization lemmaRelated: The lemma is formulated over a field, whose coefficients enable the required changes of generators.Skolem–Noether theoremRelated: The base field and its extensions set the scalars for the algebras and embeddings.Dieudonné's theoremRelated: Different fields can have different automorphisms, changing which semilinear symmetries are possible.