Statements (21)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appearsIn |
gptkb:algebraic_geometry
gptkb:Algebraic_Number_Theory |
| gptkbp:contrastsWith |
Irreducible Element
|
| gptkbp:defines |
An element p of an integral domain is prime if whenever p divides ab, then p divides a or p divides b.
|
| gptkbp:distinctFrom |
Irreducible Element (in general domains)
|
| gptkbp:example |
2 is a prime element in the ring of integers.
x is a prime element in the polynomial ring Z[x]. |
| gptkbp:field |
gptkb:Abstract_Algebra
|
| gptkbp:generalizes |
gptkb:Prime_Number
|
| https://www.w3.org/2000/01/rdf-schema#label |
Prime Elements
|
| gptkbp:property |
In a unique factorization domain, prime and irreducible elements coincide.
Every prime element is irreducible in an integral domain. |
| gptkbp:relatedTo |
gptkb:Prime_Number
Integral Domain Irreducible Element |
| gptkbp:usedIn |
gptkb:Number_Theory
gptkb:Commutative_Algebra Ring Theory |
| gptkbp:bfsParent |
gptkb:Fantastic_Four_#577
|
| gptkbp:bfsLayer |
6
|