the ring of polynomials K[x] over a field K
GPTKB entity
Statements (28)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:King
gptkb:algebra |
| gptkbp:coefficientField |
K
|
| gptkbp:contains |
K
|
| gptkbp:hasDegreeFunction |
deg(f)
|
| gptkbp:hasElementForm |
a_0 + a_1 x + a_2 x^2 + ... + a_n x^n
|
| gptkbp:hasIdealStructure |
principal ideals
|
| gptkbp:hasIndeterminate |
x
|
| gptkbp:hasQuotientField |
gptkb:field_of_rational_functions_K(x)
|
| https://www.w3.org/2000/01/rdf-schema#label |
the ring of polynomials K[x] over a field K
|
| gptkbp:identityElement |
true
|
| gptkbp:isCommutative |
true
|
| gptkbp:isCountable |
true
|
| gptkbp:isEuclideanDomain |
true
|
| gptkbp:isFinitelyGeneratedAsAlgebra |
true
|
| gptkbp:isIntegralDomain |
true
|
| gptkbp:isNoetherian |
true
|
| gptkbp:isNotAField |
true
|
| gptkbp:isPrincipalIdealDomain |
true
|
| gptkbp:isUniqueFactorizationDomain |
true
|
| gptkbp:unitElement |
1
|
| gptkbp:usedIn |
gptkb:algebra
gptkb:algebraic_geometry gptkb:commutative_algebra number theory |
| gptkbp:zeroElement |
0
|
| gptkbp:bfsParent |
gptkb:PID_(Principal_Ideal_Domain)
|
| gptkbp:bfsLayer |
6
|