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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Algebraically compact group ： ウィキペディア英語版 Algebraically compact group In mathematics, in the realm of abelian group theory, a group is said to be algebraically compact if it is a direct summand of every abelian group containing it as a pure subgroup. Equivalent characterizations of algebraic compactness: * The reduced part of the group is Hausdorff and complete in the $\backslash mathbb$ adic topology. * The group is ''pure injective'', that is, injective with respect to exact sequences where the embedding is as a pure subgroup. Relations with other properties: * A torsion-free group is cotorsion if and only if it is algebraically compact. * Every injective group is algebraically compact. * Ulm factors of cotorsion groups are algebraically compact. ==External links== * (On endomorphism rings of Abelian groups ) 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「Algebraically compact group」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.