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Abelian, in mathematics, is used in many different definitions, named after Norwegian mathematician Niels Henrik Abel:

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 abelian
- Abelianisation

In Galois theory:

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

In real analysis:

- Abelian and tauberian 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, 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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Last updated on Wednesday September 10, 2008 at 01:48:45 PDT (GMT -0700)

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This article is licensed under the GNU Free Documentation License.

Last updated on Wednesday September 10, 2008 at 01:48:45 PDT (GMT -0700)

View this article at Wikipedia.org - Edit this article at Wikipedia.org - Donate to the Wikimedia Foundation

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