Statements (48)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:containsElement |
Idempotent elements (possibly)
Nilpotent elements (possibly) Units (invertible elements) Unity (if exists) Zero divisors (possibly) Zero element |
| gptkbp:definedIn |
Set with two binary operations
|
| gptkbp:example |
gptkb:Complex_numbers
Real numbers Rational numbers Integers Finite fields Polynomial rings |
| gptkbp:generalizes |
gptkb:King
gptkb:Field gptkb:Boolean_ring gptkb:Integral_domain Polynomial ring |
| gptkbp:hasAxiom |
(a * b) * c = a * (b * c)
(a + b) * c = a * c + b * c (a + b) + c = a + (b + c) a * (b + c) = a * b + a * c a * b = b * a a + (-a) = 0 a + 0 = a a + b = b + a |
| gptkbp:hasHomomorphism |
gptkb:Ring_homomorphism
|
| gptkbp:hasMorphism |
gptkb:Ring_homomorphism
|
| gptkbp:hasProperty |
Associativity of addition
Additive identity Additive inverses Associativity of multiplication Commutativity of multiplication Distributivity of multiplication over addition Multiplicative identity (optional) |
| https://www.w3.org/2000/01/rdf-schema#label |
Commutative ring
|
| gptkbp:operator |
Addition
Multiplication |
| gptkbp:studiedIn |
gptkb:Abstract_algebra
|
| gptkbp:subunit |
gptkb:Ideal
gptkb:Quotient_ring Subring |
| gptkbp:usedIn |
gptkb:Number_theory
gptkb:Algebraic_geometry gptkb:Commutative_algebra |
| gptkbp:bfsParent |
gptkb:Prime_ideal
|
| gptkbp:bfsLayer |
7
|