Linked from

The 25 pages that link to Polynomial ring, each with the reason it gives.

• PolynomialNarrower topic: It formalizes polynomial arithmetic over a chosen coefficient system.

• Algebraic geometryRelated: Its ideals encode collections of polynomial equations.

• Field (mathematics)Related: Polynomials over a field support constructions such as adjoining roots to form extensions.

• Formal power seriesRelated: Polynomials are the finite expressions that formal series extend.

• Minimal polynomialNarrower topic: The minimal polynomial is an element of the polynomial ring over its base field.

• Polynomial factorizationNarrower topic: The coefficient ring sets which constants and polynomial factors are allowed.

• Quotient ringRelated: Polynomial rings provide the standard setting for concrete quotient-ring examples.

• Ring (mathematics)Broader topic: Polynomial rings extend ring operations to formal expressions and equations.

• Commutative ringRelated: Adjoining variables builds new commutative rings and encodes algebraic equations.

• Invariant theoryRelated: Polynomial invariants form a central algebraic object in the subject.

• Unique factorization domainBroader topic: Polynomials over a field form a unique factorization domain.

• Complex multiplicationRelated: Complex multiplication can be derived from polynomials by imposing the relation x² = −1.

• IdealRelated: Polynomial ideals encode equations and relations among variables.

• Hilbert's NullstellensatzNarrower topic: The theorem’s ideals live in polynomial rings over a field.

• AKS primality testNarrower topic: AKS performs its decisive arithmetic in a polynomial ring modulo a chosen polynomial.

• Commutative propertyBroader topic: With a commutative coefficient ring, polynomial multiplication is commutative.

• Noncommutative algebraCompared with: Ordinary polynomial multiplication permits reorderings that may fail in noncommutative rings.

• Hilbert's basis theoremBroader topic: The theorem proves that adjoining finitely many indeterminates preserves Noetherianity.

• Polynomial remainder theoremNarrower topic: The theorem holds over coefficient rings where division by a monic linear polynomial is available.

• Free objectRelated: Polynomial rings freely adjoin commuting indeterminates to a coefficient ring.

• Noether normalization lemmaRelated: The subalgebra guaranteed by the lemma is a polynomial ring.

• Ring theoryBroader topic: Adjoining indeterminates creates rings central to algebraic constructions.

• Eisenstein's criterionNarrower topic: The criterion applies to polynomials over the integers and concludes irreducibility over the rationals.

• Freshman's dreamRelated: The identity applies coefficientwise in polynomial rings of characteristic p.

• Unit (ring theory)Related: Over an integral domain, its units are exactly the constant polynomials whose coefficients are units.