翻訳と辞書 Words near each other ・ Affluenza (film) ・ Affléville ・ Affo ・ Affo Erassa ・ Affogato ・ Affoltern ・ Affoltern (Zürich) ・ Affoltern am Albis ・ Affoltern am Albis railway station ・ Affoltern District ・ Affoltern im Emmental ・ Affonso Beato ・ Affonso Celso Pastore ・ Affonso Eduardo Reidy ・ Affine manifold (disambiguation) ・ Affine monoid ・ Affine plane ・ Affine plane (incidence geometry) ・ Affine pricing ・ Affine q-Krawtchouk polynomials ・ Affine representation ・ Affine root system ・ Affine shape adaptation ・ Affine space ・ Affine sphere ・ Affine term structure model ・ Affine transformation ・ Affine variety ・ Affine vector field ・ Affine-regular polygon 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 Affine monoid ： ウィキペディア英語版 Affine monoid In abstract algebra, a branch of mathematics, an affine monoid is a commutative monoid that is finitely generated, and is isomorphic to a submonoid of a free abelian group ℤ''d'', ''d'' ≥ 0. Affine monoids are closely connected to convex polyhedra, and their associated algebras are of much use in the algebraic study of these geometric objects. == Characterization == * Affine monoids are finitely generated. This means for a monoid $M$, there exists $m\_1,\; \backslash dots\; ,\; m\_n\; \backslash in\; M$ such that :$M\; =\; m\_1\backslash mathbb+\backslash dots\; +\; m\_n\backslash mathbb$. * Affine monoids are cancellative. In other words, :$x\; +\; y\; =\; x\; +\; z$ implies that $y\; =\; z$ for all $x,y,z\; \backslash in\; M$, where $+$ denotes the binary operation on the affine monoid $M$. * Affine monoids are also torsion free. For an affine monoid $M$, $nx\; =\; ny$ implies that $x\; =\; y$ for $n\; \backslash in\; \backslash mathbb$, and $x,\; y\; \backslash in\; M$. * A subset $N$ of a monoid $M$ that is itself a monoid with respect to the operation on $M$ is a submonoid of $M$. 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「Affine monoid」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.