翻訳と辞書 Words near each other ・ Quasiconvex function ・ Quasicooronga ・ Quasicravenoceras ・ Quasicrystal ・ Quasicrystal Research ・ Quasicyclotosaurus ・ Quasideterminant ・ Quasidihedral group ・ Quasielastic neutron scattering ・ Quasielastic scattering ・ Quasieulia ・ Quasieulia endela ・ Quasieulia hirsutipalpis ・ Quasieulia jaliscana ・ Quasieulia mcguffini ・ Quasifield ・ Quasigroup ・ Quasiidentity ・ Quasilinear ・ Quasilinear utility ・ Quasimellana ・ Quasimesosella ussuriensis ・ Quasimidi ・ Quasimidi Polymorph ・ Quasimidi Sirius ・ Quasimode ・ Quasimode (band) ・ Quasimodo ・ Quasimodo (disambiguation) ・ Quasimodo (magazine) 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 Quasifield ： ウィキペディア英語版 Quasifield In mathematics, a quasifield is an algebraic structure $(Q,+,\backslash cdot)$ where + and $\backslash cdot$ are binary operations on Q, much like a division ring, but with some weaker conditions. ==Definition== A quasifield $(Q,+,\backslash cdot)$ is a structure, where + and $\backslash cdot\; \backslash ,$ are binary operations on Q, satisfying these axioms : * $(Q,+)\; \backslash ,$ is a group * $(Q\_,\backslash cdot)$ is a loop, where $Q\_\; =\; Q\; \backslash setminus\; \backslash \; \backslash ,$ * $a\; \backslash cdot\; (b+c)=a\; \backslash cdot\; b+a\; \backslash cdot\; c\; \backslash quad\backslash forall\; a,b,c\; \backslash in\; Q$ (left distributivity) * $a\; \backslash cdot\; x=b\; \backslash cdot\; x+c$ has exactly one solution $\backslash forall\; a,b,c\; \backslash in\; Q,\; a\backslash neq\; b$ Strictly speaking, this is the definition of a ''left'' quasifield. A ''right'' quasifield is similarly defined, but satisfies right distributivity instead. A quasifield satisfying both distributive laws is called a semifield, in the sense in which the term is used in projective geometry. Although not assumed, one can prove that the axioms imply that the additive group $(Q,+)$ is abelian. Thus, when referring to an ''abelian quasifield'', one means that $(Q\_0,\; \backslash cdot)$ is abelian. 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「Quasifield」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.