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 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