Statements (24)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:compatibleWith |
Field (in general)
|
| gptkbp:example |
Ring of integers
Polynomial ring over a field |
| gptkbp:generalizes |
Prime field
|
| gptkbp:hasProperty |
Cancellation law holds for multiplication
Characteristic can be zero or prime Every nonzero element is not a zero divisor If ab=0, then a=0 or b=0 Multiplicative identity No zero divisors |
| https://www.w3.org/2000/01/rdf-schema#label |
Integral domain
|
| gptkbp:is_not_necessarily |
A division ring
A field |
| gptkbp:relatedTo |
gptkb:Unique_factorization_domain
gptkb:Principal_ideal_domain Euclidean domain |
| gptkbp:studiedBy |
gptkb:Ring_theory
|
| gptkbp:subset_of |
Commutative rings with unity
|
| gptkbp:type |
gptkb:Commutative_ring
|
| gptkbp:used_in |
gptkb:Abstract_algebra
|
| gptkbp:bfsParent |
gptkb:Unique_Factorization_Domain
gptkb:Prime_ideal |
| gptkbp:bfsLayer |
7
|