the field of rational numbers Q

URI: https://gptkb.org/entity/the_field_of_rational_numbers_Q
GPTKB entity
Statements (48)
Predicate Object
gptkbp:instanceOf gptkb:algebra
gptkb:Field
gptkbp:automorphismGroup trivial
gptkbp:basisOverItself 1
gptkbp:cardinality countable infinity
gptkbp:characteristic 0
gptkbp:completionLeadsTo p-adic numbers
real numbers
gptkbp:contains integers
natural numbers
fractions
gptkbp:fieldExtensionOf integers
natural numbers
gptkbp:hasSubfield complex numbers
real numbers
gptkbp:hasSubgroup complex numbers
real numbers
https://www.w3.org/2000/01/rdf-schema#label the field of rational numbers Q
gptkbp:isArchimedean true
gptkbp:isCountable true
gptkbp:isDedekindDomain false
gptkbp:isDenseIn complex numbers
real numbers
gptkbp:isEuclideanDomain false
gptkbp:isGlobalField true
gptkbp:isHilbertianField true
gptkbp:isMinimalFieldContaining integers
natural numbers
gptkbp:isNoetherian true
gptkbp:isNotAlgebraicallyClosed true
gptkbp:isNotAlgebraicClosureOfAnyProperSubfield true
gptkbp:isNotComplete true
gptkbp:isNotFiniteField true
gptkbp:isNotLocallyCompact true
gptkbp:isOrderedField true
gptkbp:isPerfectField true
gptkbp:isPID false
gptkbp:isPrincipalIdealDomain false
gptkbp:isSimple true
gptkbp:isTotallyDisconnected true
gptkbp:isTranscendenceDegreeZeroOverItself true
gptkbp:primeFieldOfCharacteristicZero true
gptkbp:symbol gptkb:Q
gptkbp:usedIn gptkb:algebra
gptkb:mathematics
number theory
gptkbp:bfsParent gptkb:the_ring_of_integers_Z
gptkbp:bfsLayer 7