Abelian

Encyclopedia : A : AB : ABE : Abelian

Abelian, in mathematics, is used in many different definitions:

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 contained in the center
Abelianisation

In Galois theory:

Abelian extension, a field extension for which the associated Galois group is abelian

In real analysis:

Abelian 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.

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