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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 Difference algebra ： ウィキペディア英語版 Difference algebra Difference algebra is a branch of mathematics concerned with the study of difference (or functional) equations from the algebraic point of view. Difference algebra is analogous to differential algebra but concerned with difference equations rather than differential equations. As an independent subject it was initiated by Joseph Ritt and his student Richard Cohn. == Difference rings, difference fields and difference algebras == A ''difference ring'' is a commutative ring $R$ together with a ring endomorphism $\backslash sigma\backslash colon\; R\backslash to\; R$. Often it is assumed that $\backslash sigma$ is injective. When $R$ is a field one speaks of a ''difference field''. A classical example of a difference field is the field $K=\backslash mathbb(x)$ of rational functions with the difference operator $\backslash sigma$ given by $\backslash sigma(f(x))=f(x+1)$. The role of difference rings in difference algebra is similar to the role of commutative rings in commutative algebra and algebraic geometry. A morphism of difference rings is a morphism of rings that commutes with $\backslash sigma$. A ''difference algebra'' over a difference field $K$ is a difference ring $R$ with a $K$-algebra structure such that $K\backslash to\; R$ is a morphism of difference rings, i.e. $\backslash sigma\backslash colon\; R\backslash to\; R$ extends $\backslash sigma\backslash colon\; K\backslash to\; K$. A difference algebra which is a field is called a ''difference field extension''. 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「Difference algebra」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.