abelian
21abelian — abe·lian …
22Abelian — 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 …
23abelian group — noun a group in which the group operation is commutative Syn: commutative group …
24Abelian group — A group in which the group operation is commutative. It is important in the study of rings and vector spaces …
25Abelian group — noun a group that satisfies the commutative law • Syn: ↑commutative group • Hypernyms: ↑group, ↑mathematical group …
26Free abelian group — In abstract algebra, a free abelian group is an abelian group that has a basis in the sense that every element of the group can be written in one and only one way as a finite linear combination of elements of the basis, with integer coefficients …
27Pre-Abelian category — In mathematics, specifically in category theory, a pre Abelian category is an additive category that has all kernels and cokernels.Spelled out in more detail, this means that a category C is pre Abelian if: # C is preadditive, that is enriched… …
28Finitely-generated abelian group — In abstract algebra, an abelian group (G,+) is called finitely generated if there exist finitely many elements x1,...,xs in G such that every x in G can be written in the form x = n1x1 + n2x2 + ... + nsxs with integers n1,...,ns. In this case, we …
29Finitely generated abelian group — In abstract algebra, an abelian group ( G ,+) is called finitely generated if there exist finitely many elements x 1,..., x s in G such that every x in G can be written in the form : x = n 1 x 1 + n 2 x 2 + ... + n s x s with integers n 1,..., n… …
30Rank of an abelian group — In mathematics, the rank, or torsion free rank, of an abelian group measures how large a group is in terms of how large a vector space over the rational numbers one would need to contain it; or alternatively how large a free abelian group it can… …
