翻訳と辞書 Words near each other ・ GroupSpaces ・ Groupthink ・ Grouptime ・ Grouptrader Networks Limited ・ GroupWise ・ Grouse ・ Grouse (disambiguation) ・ Grouse Creek ・ Grouse Creek (British Columbia) ・ Grouse Creek (Humboldt County, California) ・ Grouse Creek block ・ Grouse Creek, Utah ・ Grouse Lake Trail ・ Grouse Lodge ・ Group W ・ Group with operators ・ Group work ・ Group Workcamps Foundation ・ Group-based cryptography ・ Group-dynamic game ・ Group-envy-free ・ Group-IB ・ Group-Office ・ Group-specific antigen ・ Groupaction ・ Groupalia ・ Groupama ・ Groupama 4 ・ Groupama Arena ・ Groupama Sailing Team 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 Group with operators ： ウィキペディア英語版 Group with operators In abstract algebra, a branch of pure mathematics, the algebraic structure group with operators or Ω-group can be viewed as a group with a set Ω that operates on the elements of the group in a special way. Groups with operators were extensively studied by Emmy Noether and her school in the 1920s. She employed the concept in her original formulation of the three Noether isomorphism theorems. == Definition == A group with operators (''G'', $\backslash Omega$) can be defined as a group ''G'' together with an action of a set $\backslash Omega$ on ''G'' : :$\backslash \; \backslash Omega\; \backslash times\; G\; \backslash rightarrow\; G\; :\; (\backslash omega\; ,\; g)\; \backslash mapsto\; g^$ that is distributive relatively to the group law : :$\backslash \; (gh)^\; =\; g^\; h^.$ For each $\backslash omega\; \backslash in\; \backslash Omega$, the application :$\backslash \; g\; \backslash mapsto\; g^$ is then an endomorphism of ''G''. From this, it results that a Ω-group can also be viewed as a group ''G'' with an indexed family $(u\_)\_$ of endomorphisms of ''G''. $\backslash Omega$ is called the operator domain. The associate endomorphisms are called the homotheties of ''G''. Given two groups ''G'', ''H'' with same operator domain $\backslash Omega$, a homomorphism of groups with operators is a group homomorphism ''f'':''G''$\backslash to$''H'' satisfying :$\backslash forall\; \backslash omega\; \backslash in\; \backslash Omega,\; \backslash forall\; g\; \backslash in\; G\; :\; f(g^\backslash omega)=(f(g))^\backslash omega.$ A subgroup ''S'' of ''G'' is called a stable subgroup, $\backslash omega$-subgroup or $\backslash Omega$-invariant subgroup if it respects the homotheties, that is :$\backslash forall\; s\; \backslash in\; S,\; \backslash forall\; \backslash omega\; \backslash in\; \backslash Omega\; :\; s^\backslash omega\; \backslash in\; S.$ 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「Group with operators」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.