Mini:Abelian
Abelian, in mathematics, is used in many different definitions, named after Norwegian mathematician Niels Henrik Abel (create): In group theory (create):
- Abelian group (create), a group in which the binary operation (create) is commutative
- Category of abelian groups Ab has abelian groups as objects and group homomorphisms (create) as morphisms (create)
- Metabelian group (create) is a group where the commutator subgroup (create) is abelian
- Abelianisation (create)
In Galois theory (create):
- Abelian extension (create), a field extension for which the associated Galois group (create) is abelian
In real analysis (create):
- Abelian and tauberian theorems, used in the summation of divergent series
In functional analysis (create)
- Abelian von Neumann algebra (create), a von Neumann algebra of operators on a Hilbert space (create) in which all elements commute
In topology (create) and number theory (create)
- Abelian variety (create), a complex torus that can be embedded into projective space
- Abelian function (create), a meromorphic function (create) on an abelian variety
- Abelian integral (create), a function related to the indefinite integral (create) of a differential of the first kind
In category theory:
- Preabelian category (create) is an additive category that has all kernels (edit) and cokernels (create)
- Abelian category (create), a preabelian category in which morphisms (create) and objects can be added.