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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 P-derivation ： ウィキペディア英語版 P-derivation In mathematics, more specifically differential algebra, a ''p''-derivation (for ''p'' a prime number) on a ring ''R'', is a mapping from ''R'' to ''R'' that satisfies certain conditions outlined directly below. The notion of a ''p''-derivation is related to that of a derivation in differential algebra. ==Definition== Let ''p'' be a prime number. A ''p''-derivation or Buium derivative on a ring $R$ is a map of sets $\backslash delta:R\backslash to\; R$ that satisfies the following "product rule": :$\backslash delta\_p(ab)\; =\; \backslash delta\_p\; (a)b^p\; +\; a^p\backslash delta\_p\; (b)\; +\; p\backslash delta\_p\; (a)\backslash delta\_p\; (b)$ and "sum rule": :$\backslash delta\_p(a+b)\; =\; \backslash delta\_p\; (a)\; +\; \backslash delta\_p(b)\; +\; \backslash frac$. as well as :$\backslash delta\_p(1)\; =0$. Note that in the "sum rule" we are not really dividing by ''p'', since all the relevant binomial coefficients in the numerator are divisible by ''p'', so this definition applies in the case when $R$ has ''p''-torsion. 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「P-derivation」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.