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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 Extension and contraction of ideals ： ウィキペディア英語版 Extension and contraction of ideals In commutative algebra, the extension and contraction of ideals are operations performed on sets of ideals. == Extension of an ideal == Let ''A'' and ''B'' be two commutative rings with unity, and let ''f'' : ''A'' → ''B'' be a (unital) ring homomorphism. If $\backslash mathfrak$ is an ideal in ''A'', then $f(\backslash mathfrak)$ need not be an ideal in ''B'' (e.g. take ''f'' to be the inclusion of the ring of integers Z into the field of rationals Q). The extension $\backslash mathfrak^e$ of $\backslash mathfrak$ in ''B'' is defined to be the ideal in ''B'' generated by $f(\backslash mathfrak)$. Explicitly, :$\backslash mathfrak^e\; =\; \backslash Big\backslash$ 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「Extension and contraction of ideals」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.