Disambiguation evidence for Abelian groups via surface form
"Abelian group"
As subject (50)
Triples where this entity appears as subject under the
label "Abelian group".
| Predicate | Object |
|---|---|
| alsoKnownAs | commutative group ⓘ |
| closedUnder | finite sums of elements ⓘ |
| closedUnder | taking inverses ⓘ |
| example | complex numbers under addition ⓘ |
| example | cyclic group of order n ⓘ |
| example | finite direct product of cyclic groups ⓘ |
| example | integers under addition ⓘ |
| example | rationals under addition ⓘ |
| example | reals under addition ⓘ |
| example | torsion subgroup of a group ⓘ |
| example | vector space under addition ⓘ |
| generalizes | additive group of a ring ⓘ |
| generalizes | additive group of a vector space ⓘ |
| generalizes | cyclic group ⓘ |
| hasAxiom | associativity of group operation ⓘ |
| hasAxiom | closure under group operation ⓘ |
| hasAxiom | commutativity of group operation ⓘ |
| hasAxiom | existence of identity element ⓘ |
| hasAxiom | existence of inverses ⓘ |
| hasCategory | category of Abelian groups ⓘ |
| hasCategoryProperty | category of Abelian groups is an Abelian category ⓘ |
| hasConstruction | direct product of Abelian groups ⓘ |
| hasConstruction | direct sum of Abelian groups ⓘ |
| hasConstruction | quotient group ⓘ |
| hasIdentityElement | 0 in additive notation ⓘ |
| hasIdentityElement | e in multiplicative notation ⓘ |
| hasInvariant | primary decomposition for finite Abelian groups ⓘ |
| hasInvariant | rank of an Abelian group ⓘ |
| hasInvariant | torsion subgroup ⓘ |
| hasInverseNotation | a⁻¹ in multiplicative notation ⓘ |
| hasInverseNotation | −a in additive notation ⓘ |
| hasMorphism | group homomorphism ⓘ |
| hasOperation | binary operation usually denoted by + or · ⓘ |
| hasProperty | associative operation ⓘ |
| hasProperty | commutative operation ⓘ |
| hasProperty | identity element ⓘ |
| hasProperty | inverse elements ⓘ |
| hasStructureTheorem | finitely generated Abelian groups decompose into direct sum of cyclic groups ⓘ |
| hasSubstructure | subgroup ⓘ |
| instanceOf | algebraic structure ⓘ |
| instanceOf | group ⓘ |
| isSpecialCaseOf | group ⓘ |
| namedAfter | Niels Henrik Abel ⓘ |
| satisfiesEquation | a + b = b + a for all elements a, b ⓘ |
| usedIn | algebraic number theory ⓘ |
| usedIn | algebraic topology ⓘ |
| usedIn | category theory ⓘ |
| usedIn | homological algebra ⓘ |
| usedIn | module theory ⓘ |
| usedIn | representation theory ⓘ |