Statements (95)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:algebra
|
| gptkbp:definedIn |
commutative ring
|
| gptkbp:example |
gptkb:algebra
gptkb:polynomial_algebra quaternion algebra group algebra |
| gptkbp:field |
abstract algebra
|
| gptkbp:generalizes |
algebra over a field
|
| gptkbp:hasAxiom |
(ab)c = a(bc)
|
| gptkbp:hasProperty |
associativity
|
| gptkbp:hasSubfield |
gptkb:commutative_algebra
gptkb:division gptkb:C*-algebra gptkb:Lie_group noncommutative geometry differential algebra Jordan algebra simple algebra tensor algebra enveloping algebra graded algebra path algebra superalgebra exterior algebra infinite-dimensional algebra semisimple algebra incidence algebra finite-dimensional algebra algebra of Chern classes algebra of Grassmann numbers algebra of Laurent polynomials algebra of Lie groups algebra of Pauli matrices algebra of Pontryagin classes algebra of Stiefel-Whitney classes algebra of alternating functions algebra of bilinear forms algebra of chains algebra of characteristic classes algebra of cochains algebra of cohomology algebra of complex numbers algebra of connections algebra of cubic forms algebra of curvature algebra of derivations algebra of differential operators algebra of distributions algebra of dual numbers algebra of endomorphisms algebra of formal power series algebra of functions algebra of group actions algebra of group representations algebra of homology algebra of manifolds algebra of matrices algebra of measures algebra of modules algebra of multilinear forms algebra of octonions algebra of operators algebra of polynomials algebra of polytopes algebra of power series algebra of principal bundles algebra of quadratic forms algebra of quaternions algebra of rational functions algebra of real numbers algebra of schemes algebra of sequences algebra of series algebra of sheaves algebra of simplices algebra of split-complex numbers algebra of symmetric functions algebra of varieties algebra of vector bundles algebra of vector fields |
| https://www.w3.org/2000/01/rdf-schema#label |
Associative algebra
|
| gptkbp:mayInclude |
identity element
unital non-unital |
| gptkbp:operator |
addition
multiplication |
| gptkbp:relatedTo |
gptkb:Lie_group
non-associative algebra |
| gptkbp:studiedIn |
gptkb:mathematics
|
| gptkbp:usedIn |
functional analysis
quantum mechanics representation theory ring theory |
| gptkbp:bfsParent |
gptkb:Enveloping_Algebras
|
| gptkbp:bfsLayer |
7
|