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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 Splitting field ： ウィキペディア英語版 Splitting field In abstract algebra, a splitting field of a polynomial with coefficients in a field is a smallest field extension of that field over which the polynomial ''splits'' or decomposes into linear factors. ==Definition== A splitting field of a polynomial ''p''(''X'') over a field ''K'' is a field extension ''L'' of ''K'' over which ''p'' factors into linear factors :$p(X)\; =\; \backslash prod\_^\; (X\; -\; a\_i)$ where for each $i$ we have $(X\; -\; a\_i)\; \backslash in\; L()$ and such that the roots ''ai'' generate ''L'' over ''K''. The extension ''L'' is then an extension of minimal degree over ''K'' in which ''p'' splits. It can be shown that such splitting fields exist and are unique up to isomorphism. The amount of freedom in that isomorphism is known as the Galois group of ''p'' (if we assume it is separable). 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「Splitting field」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.