title: Abelian
text: # Abelian
  
  Abelian may refer to:
  
  ## 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
  