Statements (49)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:alsoKnownAs |
Abelian group (in additive notation)
|
| gptkbp:example |
The complex numbers under addition
The integers under addition The rational numbers under addition The real numbers under addition |
| gptkbp:hasAxiom |
Closure under addition
Associativity of addition Commutativity of addition Existence of additive identity Existence of additive inverse |
| gptkbp:hasInverseElement |
Additive inverse
|
| gptkbp:hasSubgroup |
Abelian group
|
| https://www.w3.org/2000/01/rdf-schema#label |
Additive group
|
| gptkbp:identityElement |
Zero
|
| gptkbp:isAssociative |
true
|
| gptkbp:isCommutative |
true
|
| gptkbp:isMatrixGroup |
true
|
| gptkbp:notation |
(G, +)
|
| gptkbp:operator |
Addition
|
| gptkbp:usedFor |
gptkb:Algebraic_K-theory
gptkb:Algebraic_topology gptkb:Number_theory gptkb:Algebraic_geometry gptkb:Group_theory gptkb:Lie_groups gptkb:Representation_theory gptkb:Algebraic_number_theory Category theory Homological algebra Cryptography Functional analysis Mathematical physics Coding theory Group cohomology Cohomology groups Topological groups Algebraic combinatorics Defining fields Defining modules Defining rings Defining vector spaces Homomorphisms |
| gptkbp:usedIn |
gptkb:Linear_algebra
gptkb:Vector_spaces gptkb:Ring_theory Module theory |
| gptkbp:bfsParent |
gptkb:Algebraic_groups
|
| gptkbp:bfsLayer |
7
|