Linked from

The 29 pages that link to Field (mathematics), each with the reason it gives.

• Vector spaceRelated: Scalars come from a field, whose operations make scalar multiplication coherent.

• Finite fieldNarrower topic: Finite fields are precisely fields whose underlying sets have finitely many elements.

• Quadratic formRelated: The underlying field affects diagonalization and whether a symmetric matrix represents the form.

• Linear combinationNarrower topic: The coefficient scalars are usually drawn from a field.

• Évariste GaloisRelated: Fields provide the number systems in which polynomial roots and their symmetries are studied.

• Dual spaceRelated: The scalar field supplies the values taken by every functional in the dual.

• Galois theoryNarrower topic: Galois theory compares fields arranged inside algebraic extensions.

• Ring (mathematics)Compared with: Fields satisfy stronger division properties than general rings.

• Commutative ringBroader topic: Fields add universal nonzero invertibility to the commutative-ring structure.

• Algebraic closureNarrower topic: Algebraic closure begins with a field whose polynomials and extensions are being considered.

• Scalar multiplicationRelated: Scalars come from a field, such as the real or complex numbers.

• Algebraic curveRelated: The coefficient field affects which points and geometric features a curve possesses.

• Complex multiplicationNarrower topic: Complex numbers form a field, so multiplication obeys familiar arithmetic laws.

• Division ringCompared with: A field satisfies the same inverse condition but also requires commutative multiplication.

• Frobenius endomorphismNarrower topic: Frobenius is defined on fields, where its preservation of operations makes it an endomorphism.

• Rational pointRelated: The chosen field determines which coordinates count as rational.

• Algebraically closed fieldNarrower topic: Algebraic closure is a property of fields, defined through polynomials with coefficients in them.

• Field automorphismNarrower topic: Automorphisms act on fields while preserving their defining operations.

• Leopold KroneckerRelated: Fields provide the setting for algebraic numbers and Kronecker’s results on equations.

• Local ringRelated: Quotients by maximal ideals are fields, including the residue field of a local ring.

• Commutative propertyBroader topic: Both addition and multiplication in a field are commutative.

• Division by zeroNarrower topic: Field axioms explicitly exclude zero from the elements that may be divided by.

• Number (mathematics)Narrower topic: Fields state the shared arithmetic laws satisfied by rational, real, and complex numbers.

• Polynomial remainder theoremRelated: Fields provide the familiar setting for polynomial division and the theorem.

• Algebra over a fieldRelated: Its elements provide the scalars used to define the algebra.

• Tits alternativeRelated: Linear groups are formed from matrices over a field.

• Carmichael's theoremNarrower topic: The theorem applies to multiplicative subgroups drawn from fields.

• Steinitz exchange lemmaRelated: Vector-space scalars come from a field, which permits solving for a nonzero coefficient.

• Unit (ring theory)Narrower topic: Fields are the special case where every nonzero element is a unit.