Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:contrastsWith |
Prime element
|
| gptkbp:definedIn |
gptkb:Ring_theory
|
| gptkbp:defines |
An element of a ring that is not a unit and cannot be written as a product of two non-units
|
| gptkbp:example |
2 is irreducible in the ring of integers
x^2 + 1 is irreducible in the ring of polynomials over the real numbers |
| gptkbp:field |
gptkb:Abstract_algebra
|
| https://www.w3.org/2000/01/rdf-schema#label |
Irreducible element
|
| gptkbp:property |
Every prime element is irreducible in an integral domain
Not every irreducible element is prime |
| gptkbp:relatedTo |
gptkb:Unique_factorization_domain
gptkb:Integral_domain Prime element |
| gptkbp:usedIn |
gptkb:Commutative_algebra
gptkb:Algebraic_number_theory Factorization theory |
| gptkbp:bfsParent |
gptkb:Unique_Factorization_Domain
|
| gptkbp:bfsLayer |
7
|