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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 Additive map ： ウィキペディア英語版 Additive map In algebra an additive map, Z-linear map or additive function is a function that preserves the addition operation: : $f(x\; +\; y)\; =\; f(x)\; +\; f(y)\; .$ for any two elements ''x'' and ''y'' in the domain. For example, any linear map is additive. When the domain is the real numbers, this is Cauchy's functional equation. For a specific case of this definition, see additive polynomial. Any homomorphism ''f'' between abelian groups is additive by this definition. More formally, an additive map of ring $R\_1$ into ring $R\_2$ is a homomorphism : $f:R\_1\backslash to\; R\_2\; \backslash ,\; ,$ of the additive group of $R\_1$ into the additive group of $R\_2$. An additive map is not required to preserve the product operation of the ring. If $f$ and $g$ are additive maps, then the map $f+g$ (defined pointwise) is additive. == Additive map of a division ring == Let $D$ be a division ring of characteristic $0$. We can represent an additive map $f:D\backslash to\; D$ of the division ring $D$ as : $f(x)=\_f\; \backslash ,\; .$ We assume a sum over the index $s$. The number of items depends on the function $f$. The expressions $\_f\; \backslash in\; D$ are called the components of the additive map. 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「Additive map」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.