Statements (39)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
Euclidean domain commutative ring integral domain principal ideal domain unique factorization domain |
| gptkbp:characteristic |
0
|
| gptkbp:containsElement |
2
0 1 -1 -2 |
| gptkbp:hasUnitGroup |
{1, -1}
|
| https://www.w3.org/2000/01/rdf-schema#label |
The ring of integers Z
|
| gptkbp:isCountable |
true
|
| gptkbp:isDedekindDomain |
true
|
| gptkbp:isDiscreteValuationRing |
false
|
| gptkbp:isFinite |
false
|
| gptkbp:isNoetherian |
true
|
| gptkbp:isSimpleRing |
false
|
| gptkbp:isSubringOf |
gptkb:field_of_rational_numbers_Q
|
| gptkbp:isTotallyOrdered |
true
|
| gptkbp:isUnital |
true
|
| gptkbp:isUniversalInitialObject |
category of rings
category of Dedekind domains category of Euclidean domains category of Noetherian rings category of commutative rings category of countable rings category of infinite rings category of integral domains category of principal ideal domains category of rings with characteristic 0 category of rings with unit group {1, -1} category of totally ordered rings category of unique factorization domains category of unital rings |
| gptkbp:bfsParent |
gptkb:Noetherian_ring_(in_the_commutative_case)
|
| gptkbp:bfsLayer |
7
|