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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 Kummer ring ： ウィキペディア英語版 Kummer ring In abstract algebra, a Kummer ring $\backslash mathbb()$ is a subring of the ring of complex numbers, such that each of its elements has the form :$n\_0\; +\; n\_1\; \backslash zeta\; +\; n\_2\; \backslash zeta^2\; +\; ...\; +\; n\_\; \backslash zeta^\backslash$ where ζ is an ''m''th root of unity, i.e. :$\backslash zeta\; =\; e^\; \backslash$ and ''n''0 through ''n''''m''−1 are integers. A Kummer ring is an extension of $\backslash mathbb$, the ring of integers, hence the symbol $\backslash mathbb()$. Since the minimal polynomial of ζ is the ''m''th cyclotomic polynomial, the ring $\backslash mathbb()$ is an extension of degree $\backslash phi(m)$ (where φ denotes Euler's totient function). An attempt to visualize a Kummer ring on an Argand diagram might yield something resembling a quaint Renaissance map with compass roses and rhumb lines. The set of units of a Kummer ring contains $\backslash$. By Dirichlet's unit theorem, there are also units of infinite order, except in the cases , (in which case we have the ordinary ring of integers), the case (the Gaussian integers) and the cases , (the Eisenstein integers). Kummer rings are named after Ernst Kummer, who studied the unique factorization of their elements. ==See also== * Kummer theory 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「Kummer ring」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.