**Abelian** — 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 … Wikipedia

**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 group** — [ə bē′lē ən, əbēl′yən] n. 〚after Niels H. Abel (1802 29), Norw mathematician〛 Math. a commutative group * * * … Universalium

**Abelian group** — [ə bē′lē ən, əbēl′yən] n. [after Niels H. Abel (1802 29), Norw mathematician] Math. a commutative group … English World dictionary

**Abelian group** — For other uses, see Abelian (disambiguation). Abelian group is also an archaic name for the symplectic group Concepts in group theory category of groups subgroups, normal subgroups group homomorphisms, kernel, image, quotient direct product,… … Wikipedia

**Abelian variety** — In mathematics, particularly in algebraic geometry, complex analysis and number theory, an Abelian variety is a projective algebraic variety that is at the same time an algebraic group, i.e., has a group law that can be defined by regular… … Wikipedia

**Abelian category** — In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties. The motivating prototype example of an abelian category is the category of… … Wikipedia