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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): : where the ''pi'' are distinct primes, then Z/''n''Z is naturally isomorphic to the product ring : 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
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