abelian
31Arithmetic of abelian varieties — In mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or family of those. It goes back to the studies of Fermat on what are now recognised as elliptic curves; and has become a very… …
32Dual abelian variety — In mathematics, a dual abelian variety can be defined from an abelian variety A, defined over a field K. Contents 1 Definition 2 History 3 Dual isogeny (elliptic curve case) …
33Non-abelian class field theory — In mathematics, non abelian class field theory is a catchphrase, meaning the extension of the results of class field theory, the relatively complete and classical set of results on abelian extensions of any number field K, to the general Galois… …
34Timeline of abelian varieties — This is a timeline of the theory of abelian varieties in algebraic geometry, including elliptic curves.Early history* c. 1000 Al Karaji writes on congruent numbers [ [http://www.cms.math.ca/Events/summer05/abs/pdf/hm.pdf PDF] ] eventeenth… …
35Category of abelian groups — In mathematics, the category Ab has the abelian groups as objects and group homomorphisms as morphisms. This is the prototype of an abelian category.The monomorphisms in Ab are the injective group homomorphisms, the epimorphisms are the… …
36Torsion-free abelian groups of rank 1 — Infinitely generated abelian groups have very complex structure and are far less well understood than finitely generated abelian groups. Even torsion free abelian groups are vastly more varied in their characteristics than vector spaces. Torsion… …
37Equations defining abelian varieties — In mathematics, the concept of abelian variety is the higher dimensional generalization of the elliptic curve. The equations defining abelian varieties are a topic of study because every abelian variety is a projective variety. In dimension d ge; …
38Elementary abelian group — In group theory an elementary abelian group is a finite abelian group, where every nontrivial element has order p where p is a prime.By the classification of finitely generated abelian groups, every elementary abelian group must be of the form:(… …
39Non-abelian group — In mathematics, a non abelian group, also sometimes called a non commutative group, is a group (G, * ) in which there are at least two elements a and b of G such that a * b ≠ b * a.[1][2] The term non abelian is …
40Norm (abelian group) — In mathematics, specifically abstract algebra, if (G, •) is an abelian group then ν : G → ℝ is said to be a norm on the abelian group (G, •) if: ν(g) > 0 if g ≠ 0, ν(g • h) ≤ ν(g) + ν(h), ν(mg) = |m|ν(g) if m ∈ ℤ. The norm ν is discrete… …
