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