Editing Abelian

{{wiktionary|Abelian|abelian}}
'''Abelian''' may refer to:
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==Mathematics==
===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]], a group where the commutator subgroup is abelian
* [[Abelianisation]]

===Topology and number theory===
* [[Abelian variety]], a complex torus that can be embedded into projective space
* [[Abelian surface]], a two-dimensional abelian variety
* [[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

===Other mathematics===
* [[Abelian category]], in category theory, a preabelian category in which every monomorphism is a kernel and every epimorphism is a cokernel
* [[Abelian and Tauberian theorems]], in real analysis, used in the summation of divergent series
* [[Abelian extension]], in Galois theory, a field extension for which the associated Galois group is abelian
* [[Abelian von Neumann algebra]], in functional analysis, a von Neumann algebra of operators on a Hilbert space in which all elements commute

==Other uses==
* Abelian, in physics, a [[gauge theory]] with a commutative symmetry group
* [[Hovhannes Abelian]] (1865–1936), Armenian actor
* [[Movses Abelian]], Armenian diplomat

==See also==
* [[Pre-abelian category]], an additive category that has all kernels and cokernels
* [[Niels Henrik Abel]] (1802–1829), Norwegian mathematician who gave his name to several different mathematical concepts
* [[Abelians]], a 4th-century Christian sect
** [[Abel]], a Biblical figure in the Book of Genesis

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