abelian
1Abelian — 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 …
2Abelian — 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 …
3abelian — adjective Having a commutative defining operation. See Also: abelian algebra, abelian group, abelian operation, abelian ring …
4abelian — adjective Usage: often capitalized Etymology: Niels Abel died 1829 Norwegian mathematician Date: 1847 commutative 2 < abelian group > < abelian ring > …
5abelian — 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 …
6Abelian — /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;… …
7Abelian group — [ə bē′lē ən, əbēl′yən] n. 〚after Niels H. Abel (1802 29), Norw mathematician〛 Math. a commutative group * * * …
8Abelian group — [ə bē′lē ən, əbēl′yən] n. [after Niels H. Abel (1802 29), Norw mathematician] Math. a commutative group …
9Abelian 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,… …
10Abelian 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… …
