Prime ideal

URI: https://gptkb.org/entity/Prime_ideal

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:mathematical_concept
gptkbp:category	gptkb:Ideal_theory
gptkbp:definedIn	gptkb:Ring_theory
gptkbp:field	gptkb:Commutative_algebra gptkb:Abstract_algebra
gptkbp:firstAppearance	gptkb:19th_century
gptkbp:generalizes	gptkb:Prime_number
gptkbp:hasSubgroup	gptkb:Ideal
gptkbp:inRing	gptkb:Commutative_ring
gptkbp:introduced	gptkb:Richard_Dedekind
gptkbp:notableExample	(0) in an integral domain (p) in Z, where p is a prime number
gptkbp:property	If ab ∈ P, then a ∈ P or b ∈ P
gptkbp:quotientRing	gptkb:Integral_domain
gptkbp:relatedConcept	gptkb:Primary_ideal gptkb:Radical_ideal gptkb:Maximal_ideal
gptkbp:symbol	P
gptkbp:usedIn	gptkb:Algebraic_geometry gptkb:Algebraic_number_theory
gptkbp:bfsParent	gptkb:Ideal
gptkbp:bfsLayer	6
https://www.w3.org/2000/01/rdf-schema#label	Prime ideal