|
gptkbp:instanceOf
|
Algebraic Structure
|
|
gptkbp:basisFor
|
Monomials
|
|
gptkbp:canBeMultivariate
|
true
|
|
gptkbp:canBeUnivariate
|
true
|
|
gptkbp:characteristic
|
Same as R
|
|
gptkbp:definedIn
|
gptkb:King
|
|
gptkbp:field
|
gptkb:Abstract_Algebra
|
|
gptkbp:generalizes
|
Field of Rational Functions
Ring of Integers
|
|
gptkbp:hasApplication
|
gptkb:Algebraic_Coding_Theory
gptkb:algebraic_geometry
gptkb:Number_Theory
gptkb:Invariant_Theory
gptkb:Coding_Theory
gptkb:Commutative_Algebra
Cryptography
Combinatorics
Interpolation
Computer Algebra
Symbolic Computation
Factorization
Constructing Field Extensions
Groebner Bases
Solving Polynomial Equations
|
|
gptkbp:hasDegreeFunction
|
true
|
|
gptkbp:hasHomomorphism
|
Evaluation Homomorphism
|
|
gptkbp:hasIdealStructure
|
Principal Ideal Domain if R is Field
|
|
gptkbp:hasQuotientStructure
|
Quotient Ring
|
|
gptkbp:hasType
|
Polynomial
|
|
gptkbp:hasZeroDivisorsIf
|
R has Zero Divisors
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
Polynomial Ring
|
|
gptkbp:identityElement
|
true
|
|
gptkbp:isCommutative
|
true
|
|
gptkbp:isEuclideanDomainIf
|
R is Field
|
|
gptkbp:isFinitelyGeneratedAsAlgebra
|
true
|
|
gptkbp:isGradedRing
|
true
|
|
gptkbp:isIntegralDomainIf
|
R is Integral Domain
|
|
gptkbp:isNoetherian
|
true
|
|
gptkbp:isUniversalObject
|
true
|
|
gptkbp:notation
|
R[x]
|
|
gptkbp:operator
|
Addition
Multiplication
|
|
gptkbp:subunit
|
gptkb:Ideal
Subring
Monomial
|
|
gptkbp:usedIn
|
gptkb:algebraic_geometry
gptkb:Number_Theory
gptkb:Coding_Theory
gptkb:Commutative_Algebra
|
|
gptkbp:bfsParent
|
gptkb:Polynomial_Functions
|
|
gptkbp:bfsLayer
|
7
|