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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 Ideal theory ： ウィキペディア英語版 Ideal theory ==In mathematics== In mathematics, ''ideal theory'' is the theory of ideals in commutative rings; and is the precursor name for the contemporary subject of commutative algebra. The name grew out of the central considerations, such as the Lasker–Noether theorem in algebraic geometry, and the ideal class group in algebraic number theory, of the commutative algebra of the first quarter of the twentieth century. It was used in the influential van der Waerden text on abstract algebra from around 1930. The ideal theory in question had been based on elimination theory, but in line with David Hilbert's taste moved away from algorithmic methods. Gröbner basis theory has now reversed the trend, for computer algebra. The importance of the ideal in general of a module, more general than an ''ideal'', probably led to the perception that ''ideal theory'' was too narrow a description. Valuation theory, too, was an important technical extension, and was used by Helmut Hasse and Oscar Zariski. Bourbaki used ''commutative algebra''; sometimes ''local algebra'' is applied to the theory of local rings. D. G. Northcott's 1953 Cambridge Tract ''Ideal Theory'' (reissued 2004 under the same title) was one of the final appearances of the name. 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「Ideal theory」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.