翻訳と辞書 Words near each other ・ Structure of the Spanish Army ・ Structure of the stage in bunraku ・ Structure of the United States Air Force ・ Structure of the United States Armed Forces ・ Structure of the United States Army ・ Structure of the United States Congress ・ Structure of the United States Navy ・ Structure plan ・ Structure preservation principle ・ Structure relocation ・ Structure space ・ Structure specific recognition protein 1 ・ Structure tensor ・ Structure the Spin Dr. ・ Structure theorem ・ Structure theorem for finitely generated modules over a principal ideal domain ・ Structure theorem for Gaussian measures ・ Structure validation ・ Structure, sequence and organization ・ Structure, Sign, and Play in the Discourse of the Human Sciences ・ Structure-based assignment ・ Structured academy controversy ・ Structured analysis ・ Structured Analysis and Design Technique ・ Structured ASIC platform ・ Structured Audio Orchestra Language ・ Structured cabling ・ Structured Clinical Interview for DSM-IV ・ Structured cognitive behavioral training ・ Structured collar 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 Structure theorem for finitely generated modules over a principal ideal domain ： ウィキペディア英語版 Structure theorem for finitely generated modules over a principal ideal domain In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that finitely generated modules can be uniquely decomposed in much the same way that integers have a prime factorization. The result provides a simple framework to understand various canonical form results for square matrices over fields. ==Statement== When a vector space over a field ''F'' has a finite generating set, then one may extract from it a basis consisting of a finite number ''n'' of vectors, and the space is therefore isomorphic to ''Fn''. The corresponding statement with the ''F'' generalized to a principal ideal domain ''R'' is no longer true, as a finitely generated module over ''R'' need not have any basis. However such a module is still isomorphic to a quotient of some module ''Rn'' with ''n'' finite (to see this it suffices to construct the morphism that sends the elements of the canonical basis ''Rn'' to the generators of the module, and take the quotient by its kernel.) By changing the choice of generating set, one can in fact describe the module as the quotient of some ''Rn'' by a particularly simple submodule, and this is the structure theorem. The structure theorem for finitely generated modules over a principal ideal domain usually appears in the following two forms. 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「Structure theorem for finitely generated modules over a principal ideal domain」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.