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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 Product of rings ： ウィキペディア英語版 Product of rings In mathematics, it is possible to combine several rings into one large product ring. This is done as follows: if ''I'' is some index set and ''Ri'' is a ring for every ''i'' in ''I'', then the cartesian product can be turned into a ring by defining the operations coordinate-wise. The resulting ring is called a direct product of the rings ''R''''i''. The direct product of finitely many rings coincides with the direct sum of rings. ==Examples== An important example is the ring Z/''n''Z of integers modulo ''n''. If ''n'' is written as a product of prime powers (see fundamental theorem of arithmetic): :$n=p\_1^\backslash \; p\_2^\backslash \; \backslash cdots\backslash \; p\_k^$ where the ''pi'' are distinct primes, then Z/''n''Z is naturally isomorphic to the product ring :$\backslash mathbf/p\_1^\backslash mathbf\; \backslash \; \backslash times\; \backslash \; \backslash mathbf/p\_2^\backslash mathbf\; \backslash \; \backslash times\; \backslash \; \backslash cdots\; \backslash \; \backslash times\; \backslash \; \backslash mathbf/p\_k^\backslash mathbf$ This follows from the Chinese remainder theorem. 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「Product of rings」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.