PID (Principal Ideal Domain)
GPTKB entity
Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
integral domain |
| gptkbp:defines |
an integral domain in which every ideal is principal
|
| gptkbp:example |
gptkb:the_ring_of_integers_Z
gptkb:the_ring_of_polynomials_K[x]_over_a_field_K gptkb:the_ring_of_polynomials_in_two_variables_K[x,y] |
| https://www.w3.org/2000/01/rdf-schema#label |
PID (Principal Ideal Domain)
|
| gptkbp:isA |
commutative ring
|
| gptkbp:namedFor |
gptkb:Richard_Dedekind
|
| gptkbp:property |
every PID is a Noetherian ring
every PID is a unique factorization domain every ideal can be generated by a single element |
| gptkbp:relatedConcept |
gptkb:Dedekind_domain
Noetherian ring Euclidean domain unique factorization domain |
| gptkbp:usedIn |
gptkb:algebraic_geometry
gptkb:commutative_algebra abstract algebra algebraic number theory |
| gptkbp:bfsParent |
gptkb:commutative_algebra
|
| gptkbp:bfsLayer |
5
|