Statements (18)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:appliesTo |
integral domains
|
| gptkbp:concerns |
polynomials
unique factorization domains |
| gptkbp:field |
gptkb:algebra
gptkb:commutative_algebra |
| gptkbp:implies |
irreducibility of polynomials over UFDs
|
| gptkbp:namedAfter |
gptkb:Carl_Friedrich_Gauss
|
| gptkbp:publishedIn |
gptkb:Disquisitiones_Arithmeticae
|
| gptkbp:relatedTo |
gptkb:Eisenstein's_criterion
Gauss's lemma (number theory) |
| gptkbp:state |
A polynomial over a UFD is primitive if and only if it is irreducible over the field of fractions
If R is a unique factorization domain, then so is R[x] |
| gptkbp:usedIn |
proof of the fundamental theorem of algebra
proof of unique factorization in polynomial rings |
| gptkbp:bfsParent |
gptkb:Karl_Friedrich_Gauss
|
| gptkbp:bfsLayer |
8
|
| https://www.w3.org/2000/01/rdf-schema#label |
Gauss's lemma (polynomials)
|