翻訳と辞書 Words near each other ・ Rural Institute of Higher Studies ・ Rural Institute of Medical Sciences and Research ・ Rural Internet ・ Rural Khmer house ・ Rural King ・ Rural Land Register ・ Ruptawa ・ Ruptela ・ Ruptiliocarpon ・ Ruptly ・ Ruptura ・ Rupture ・ Rupture (band) ・ Rupture (social networking) ・ Rupture disc ・ Rupture field ・ Rupture of membranes ・ Ruptured Heart Theory ・ Rupununi ・ Rupununi savannah ・ Rupununi Uprising ・ Ruputer ・ Rupwal ・ Rupyal ・ Rupéreux ・ Rupčine ・ Ruqaiya Hasan ・ Ruqaiya Sultan Begum ・ Ruqaiyyah Waris Maqsood ・ Ruqaya Al-Ghasra Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Rupture field ： ウィキペディア英語版 Rupture field In abstract algebra, a rupture field of a polynomial $P(X)$ over a given field $K$ such that $P(X)\backslash in\; K()$ is a field extension of $K$ generated by a root $a$ of $P(X)$.〔 〕 For instance, if $K=\backslash mathbb\; Q$ and $P(X)=X^3-2$ then $\backslash mathbb\; Q$ is a rupture field for $P(X)$. The notion is interesting mainly if $P(X)$ is irreducible over $K$. In that case, all rupture fields of $P(X)$ over $K$ are isomorphic, non canonically, to $K\_P=K()/(P(X))$: if $L=K()$ where $a$ is a root of $P(X)$, then the ring homomorphism $f$ defined by $f(k)=k$ for all $k\backslash in\; K$ and $f(X\backslash mod\; P)=a$ is an isomorphism. Also, in this case the degree of the extension equals the degree of $P$. A rupture field of a polynomial does not necessarily contain all the roots of that polynomial: in the above example the field $\backslash mathbb\; Q$ does not contain the other two (complex) roots of $P(X)$ (namely $\backslash omega\backslash sqrt()2$ and $\backslash omega^2\backslash sqrt()2$ where $\backslash omega$ is a primitive third root of unity). For a field containing all the roots of a polynomial, see the splitting field. ==Examples== A rupture field of $X^2+1$ over $\backslash mathbb\; R$ is $\backslash mathbb\; C$. It is also a splitting field. The rupture field of $X^2+1$ over $\backslash mathbb\; F\_3$ is $\backslash mathbb\; F\_9$ since there is no element of $\backslash mathbb\; F\_3$ with square equal to $-1$ (and all quadratic extensions of $\backslash mathbb\; F\_3$ are isomorphic to $\backslash mathbb\; F\_9$). 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「Rupture 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.