- Abelian
**Abelian**, in mathematics, is used in many different definitions, named after Norwegian mathematicianNiels Henrik Abel :In

**group theory:***

Abelian group , a group in which the binary operation iscommutative

**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 abelianIn

**real analysis:***

Abelian and tauberian theorems , used in the summation of divergent seriesIn

**functional analysis***

Abelian von Neumann algebra , a von Neumann algebra of operators on a Hilbert space in which all elements commuteIn

**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 kindIn

**category theory**:*

Preabelian category , an additive category that has all kernels and cokernels

*Abelian category , a preabelian category in which every monomorphism is a kernel and every epimorphism is a cokernel

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