翻訳と辞書 Words near each other ・ Moe Ankney ・ Moe anthropomorphism ・ Moe Aung Yin ・ Moe Baby Blues ・ Moe Bandy ・ Moe Barr ・ Moe Becker ・ Moe Berg ・ Moe Berg (musician) ・ Moe book ・ Moe Brooker ・ Moe Brothers ・ Module (mathematics) ・ Module (musician) ・ Module file ・ Module homomorphism ・ Module Marketplace ・ Module of covariants ・ Module pattern ・ Module spectrum ・ Modulf Aukan ・ Moduli (physics) ・ Moduli of algebraic curves ・ Moduli scheme ・ Moduli space ・ Moduli stack of formal group laws ・ Moduli stack of principal bundles ・ Modulidae ・ Modulin ・ Modulo 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 Module homomorphism ： ウィキペディア英語版 Module homomorphism In algebra, a module homomorphism is a function between modules that preserves module structures. Explicitly, if ''M'' and ''N'' are left modules over a ring ''R'', then a function $f:\; M\; \backslash to\; N$ is called a module homomorphism or a ''R''-linear map if for any ''x'', ''y'' in ''M'' and ''r'' in ''R'', :$f(x\; +\; y)\; =\; f(x)\; +\; f(y),$ :$f(rx)\; =\; rf(x).$ If ''M'', ''N'' are right module, then the second condition is replaced with ::$f(xr)\; =\; f(x)r.$ The pre-image of the zero element under ''f'' is called the kernel of ''f''. The set of all module homomorphisms from ''M'' to ''N'' is denoted by Hom''R''(''M'', ''N''). It is an abelian group but is not necessarily a module unless ''R'' is commutative. The isomorphism theorems hold for module homomorphisms. == Examples == *$\backslash operatorname\_/n,\; \backslash mathbb/m)\; =\; \backslash mathbb/\backslash operatorname(n,m)$. *For any ring ''R'', * *$\backslash operatorname\_R(R)\; =\; R$ as rings when ''R'' is viewed as a right module over itself. * *$\backslash operatorname\_R(R,\; M)\; =\; M$ through $f\; \backslash mapsto\; f(1)$ for any left module ''M''. * *$\backslash operatorname\_R(M,\; R)$ is called the dual module of ''M''; it is a left (resp. right) module if ''M'' is a right (resp. left) module over ''R'' with the module structure coming from the ''R''-action on ''R''. It is denoted by $M^$ *. 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「Module homomorphism」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.