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Torsion-free abelian groups of rank 1 : ウィキペディア英語版 | Torsion-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-free abelian groups of rank 1 are far more amenable than those of higher rank, and a satisfactory classification exists, even though there are an uncountable number of isomorphism classes. ==Definition==
A torsion-free abelian group of rank 1 is an abelian group such that every element except the identity has infinite order, and for any two non-identity elements ''a'' and ''b'' there is a non-trivial relation between them over the integers: :
抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Torsion-free abelian groups of rank 1」の詳細全文を読む
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