Statements (14)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
polynomials
integers unique factorization domains |
| gptkbp:field |
gptkb:algebra
number theory |
| https://www.w3.org/2000/01/rdf-schema#label |
Eisenstein's criterion
|
| gptkbp:namedAfter |
gptkb:Ferdinand_Eisenstein
|
| gptkbp:publishedIn |
1844
|
| gptkbp:state |
If there exists a prime p such that p divides all coefficients except the leading one, p does not divide the leading coefficient, and p^2 does not divide the constant term, then the polynomial is irreducible over the rationals.
|
| gptkbp:usedFor |
irreducibility testing
|
| gptkbp:bfsParent |
gptkb:Cyclotomic_fields
gptkb:Commutative_Algebra |
| gptkbp:bfsLayer |
8
|