Statements (90)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:additionHasIdentity |
yes
|
| gptkbp:additionHasInverses |
yes
|
| gptkbp:additionIs |
associative
commutative |
| gptkbp:defines |
set equipped with two binary operations satisfying certain axioms
|
| gptkbp:distributiveLaw |
multiplication distributes over addition
|
| gptkbp:example |
polynomial ring
integers matrix ring function ring modular arithmetic ring |
| gptkbp:generalizes |
gptkb:Field
gptkb:Boolean_ring commutative ring integral domain division ring matrix ring |
| gptkbp:hasApplication |
gptkb:algebraic_geometry
coding theory computer science cryptography number theory physics combinatorics |
| gptkbp:hasProperty |
associativity
distributivity commutativity of addition zero element additive inverse may be commutative may be noncommutative may be without zero divisors may have unity may have zero divisors may lack unity multiplicative identity (optional) multiplicative inverse (not required) |
| https://www.w3.org/2000/01/rdf-schema#label |
Ring (mathematics)
|
| gptkbp:introduced |
gptkb:Richard_Dedekind
|
| gptkbp:introducedIn |
19th century
|
| gptkbp:multiplicationHasIdentity |
not required
|
| gptkbp:multiplicationIs |
associative
not necessarily commutative |
| gptkbp:operator |
addition
multiplication |
| gptkbp:relatedConcept |
gptkb:group_of_people
gptkb:model gptkb:Field gptkb:Artinian_ring gptkb:C*-algebra gptkb:Jacobson_radical gptkb:Boolean_ring gptkb:von_Neumann_regular_ring Noetherian ring polynomial ring Euclidean domain commutative ring integral domain local ring power series ring principal ideal domain unique factorization domain algebra over a field commutator endomorphism ring ring homomorphism automorphism group center of a ring division ring semiring semisimple ring simple ring group ring topological ring direct product of rings matrix ring nilradical Banach ring direct sum of rings tensor product of rings |
| gptkbp:studiedIn |
gptkb:algebra
abstract algebra |
| gptkbp:subunit |
ideal
ring homomorphism quotient ring subring |
| gptkbp:bfsParent |
gptkb:Left_ideal
gptkb:Ring_isomorphism |
| gptkbp:bfsLayer |
7
|