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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 Direct sum of modules ： ウィキペディア英語版 Direct sum of modules In abstract algebra, the direct sum is a construction which combines several modules into a new, larger module. The direct sum of modules is the smallest module which contains the given modules as submodules with no "unnecessary" constraints, making it an example of a coproduct. Contrast with the direct product, which is the dual notion. The most familiar examples of this construction occur when considering vector spaces (modules over a field) and abelian groups (modules over the ring Z of integers). The construction may also be extended to cover Banach spaces and Hilbert spaces. == Construction for vector spaces and abelian groups == We give the construction first in these two cases, under the assumption that we have only two objects. Then we generalise to an arbitrary family of arbitrary modules. The key elements of the general construction are more clearly identified by considering these two cases in depth. 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「Direct sum of modules」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.