Statements (23)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:definedIn |
gptkb:Ring_theory
|
| gptkbp:defines |
An ideal generated by a single element
|
| gptkbp:example |
In Z, (6) = {..., -12, -6, 0, 6, 12, ...}
In Z, every ideal is principal |
| gptkbp:field |
gptkb:Abstract_algebra
|
| gptkbp:generation |
Single element of a ring
|
| gptkbp:hasSubgroup |
gptkb:Ideal
|
| https://www.w3.org/2000/01/rdf-schema#label |
Principal ideal
|
| gptkbp:notation |
gptkb:Ra
(a) aR |
| gptkbp:property |
Principal ideals are used in the classification of rings
Every element of the ideal is a multiple of the generator In noncommutative rings, left and right principal ideals may differ In a principal ideal domain, every ideal is principal Principal ideals are two-sided in commutative rings |
| gptkbp:relatedTo |
gptkb:King
gptkb:Ideal gptkb:Principal_ideal_domain Generator |
| gptkbp:bfsParent |
gptkb:Ideal
|
| gptkbp:bfsLayer |
6
|