field of rational functions K(x)
GPTKB entity
Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:Field
|
| gptkbp:automorphismGroup |
PGL(2,K)
|
| gptkbp:characteristic |
same as K
|
| gptkbp:contains |
K
K[x] |
| gptkbp:containsElement |
rational functions in x with coefficients in K
|
| gptkbp:definedIn |
gptkb:field_K
|
| gptkbp:extendsTo |
K
|
| https://www.w3.org/2000/01/rdf-schema#label |
field of rational functions K(x)
|
| gptkbp:isCountableIf |
K is countable
|
| gptkbp:isNotAlgebraicallyClosed |
true
|
| gptkbp:isomorphicTo |
K(y) for any transcendental y over K
|
| gptkbp:isPerfectIf |
K is perfect
|
| gptkbp:isQuotientFieldOf |
K[x]
|
| gptkbp:isSimpleExtensionOf |
K
|
| gptkbp:isUncountableIf |
K is uncountable
|
| gptkbp:transcendenceDegree |
1 over K
|
| gptkbp:usedIn |
gptkb:algebraic_geometry
field theory algebraic function theory |
| gptkbp:bfsParent |
gptkb:the_ring_of_polynomials_K[x]_over_a_field_K
|
| gptkbp:bfsLayer |
7
|