- 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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**Abelian**— A*bel i*an, Abelite A bel*ite, Abelonian A bel*o ni*an, n. (Eccl. Hist.) One of a sect in Africa (4th century), mentioned by St. Augustine, who states that they married, but lived in continence, after the manner, as they pretended, of Abel. [1913 … The Collaborative International Dictionary of English**abelian**— adjective Having a commutative defining operation. See Also: abelian algebra, abelian group, abelian operation, abelian ring … Wiktionary**abelian**— adjective Usage: often capitalized Etymology: Niels Abel died 1829 Norwegian mathematician Date: 1847 commutative 2 < abelian group > < abelian ring > … New Collegiate Dictionary**abelian**— ə¦bēlyən, lēən adjective Usage: often capitalized Etymology: Niels Abel died 1829 Norwegian mathematician + English ian : commutative 2 abelian ring the real numbers under addition comprise an abelian group … Useful english dictionary**Abelian**— /euh bee lee euhn, euh beel yeuhn/, adj. Math. 1. of or pertaining to Niels Henrik Abel or his theorems. 2. pertaining to an algebraic system in which an operation is commutative: an Abelian group. 3. pertaining to such an operation. [1905 10;… … Universalium**Abelian**— noun A member of a sect in fourth century Africa mentioned by St. Augustine, who states that they married but lived in continence after the manner, as they claimed, of Abel. Syn: Abelite, Abelonian … Wiktionary**abelián**— adj. m. (sil. li an), pl. abeliéni; f. sg. abeliánã, pl. abeliéne … Romanian orthography**abelian**— [ə bi:lɪən] adjective Mathematics (of a group) having members related by a commutative operation (i.e. a*b = b*a). Origin C19: from the name of the Norwegian mathematician Niels Henrik Abel + ian … English new terms dictionary**abelian**— abe·lian … English syllables**Abelian**— A•be•li•an [[t]əˈbi li ən, əˈbil yən[/t]] adj. math. of or pertaining to an algebraic system in which an operation is commutative • Etymology: 1905–10; after Niels Henrik Abel (1802–29), Norwegian mathematician … From formal English to slang