翻訳と辞書 Words near each other ・ Hereditary officers of the Roman Curia ・ Hereditary Order of Descendants of Colonial Governors ・ Hereditary pancreatitis ・ Hereditary peer ・ Hereditary Peerage Association ・ Hereditary persistence of fetal hemoglobin ・ Hereditary politicians ・ Hereditary Prince of Monaco ・ Hereditary Princes of Modena ・ Hereditary Princesses of Modena ・ Hereditary progressive mucinous histiocytosis ・ Hereditary property ・ Hereditary pyropoikilocytosis ・ Hereditary Quartermaster General of the Sacred Apostolic Palace ・ Hereditary Revenues Act 1856 ・ Hereditary ring ・ Hereditary sclerosing poikiloderma ・ Hereditary sensory and autonomic neuropathy ・ Hereditary sensory and autonomic neuropathy type I ・ Hereditary set ・ Hereditary spastic paraplegia ・ Hereditary spherocytosis ・ Hereditary stomatocytosis ・ Hereditary title ・ Hereditary witch ・ Hereditas ・ Heredity ・ Heredity (album) ・ Heredity (disambiguation) ・ Heredity (film) 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 Hereditary ring ： ウィキペディア英語版 Hereditary ring In mathematics, especially in the area of abstract algebra known as module theory, a ring ''R'' is called hereditary if all submodules of projective modules over ''R'' are again projective. If this is required only for finitely generated submodules, it is called semihereditary. For a noncommutative ring ''R'', the terms left hereditary and left semihereditary and their right hand versions are used to distinguish the property on a single side of the ring. To be left (semi-)hereditary, all (finitely generated) submodules of projective ''left'' ''R''-modules must be projective, and to be right (semi-)hereditary all (finitely generated) submodules of projective right submodules must be projective. It is possible for a ring to be left (semi-)hereditary but not right (semi-)hereditary, and vice versa. ==Equivalent definitions== * The ring ''R'' is left (semi-)hereditary if and only if all (finitely generated) left ideals of ''R'' are projective modules. * The ring ''R'' is left hereditary if and only if all left modules have projective resolutions of length at most 1. Hence the usual derived functors such as $\backslash mathrm\_R^i$ and $\backslash mathrm\_i^R$ are trivial for $i>1$. 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「Hereditary ring」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.