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The classification theorem for finitely generated Abelian groups is well known and plays big role in mathematics.

Are there any structure theorems about infinitely generated Abelian groups known?

user26857
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V. Rogov
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    This theorem is a special case of structure theorem for finitely generated modules over PID. Some words on the non-finitely generated case can be found in the related wikipedia article https://en.wikipedia.org/wiki/Structure_theorem_for_finitely_generated_modules_over_a_principal_ideal_domain#Non-finitely_generated_modules – lisyarus Nov 28 '15 at 01:18
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    http://math.stackexchange.com/questions/313737/status-of-the-classification-of-non-finitely-generated-abelian-groups – Qiaochu Yuan Nov 28 '15 at 01:37
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    http://math.stackexchange.com/questions/22646/structure-theorem-for-abelian-torsion-groups-that-are-not-finitely-generated – Qiaochu Yuan Nov 28 '15 at 01:37
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    https://simpletonsymposium.wordpress.com/2013/05/31/countably-generated-abelian-groups/ – Qiaochu Yuan Nov 28 '15 at 01:38

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