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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 Planar ternary ring ： ウィキペディア英語版 Planar ternary ring In mathematics, an algebraic structure $(R,T)$ consisting of a non-empty set $R$ and a ternary mapping $T\; \backslash colon\; R^3\; \backslash to\; R\; \backslash ,$ may be called a ternary system. A planar ternary ring (PTR) or ternary field is special type of ternary system used by to construct projective planes by means of coordinates. A planar ternary ring is not a ring in the traditional sense. There is wide variation in the terminology. Planar ternary rings or ternary fields as defined here have been called by other names in the literature, and the term "planar ternary ring" can mean a variant of the system defined here. The term "ternary ring" often means a planar ternary ring, but it can also simply mean a ternary system. ==Definition== A planar ternary ring is a structure $(R,T)$ where $R$ is a set containing at least two distinct elements, called 0 and 1, and $T\backslash colon\; R^3\backslash to\; R\; \backslash ,$ a mapping which satisfies these five axioms: # $T(a,0,b)=T(0,a,b)=b,\backslash quad\; \backslash forall\; a,b\; \backslash in\; R$; # $T(1,a,0)=T(a,1,0)=a,\backslash quad\; \backslash forall\; a\; \backslash in\; R$; # $\backslash forall\; a,b,c,d\; \backslash in\; R,\; a\backslash neq\; c$, there is a unique $x\backslash in\; R$ such that : $T(x,a,b)=T(x,c,d)\; \backslash ,$; # $\backslash forall\; a,b,c\; \backslash in\; R$, there is a unique $x\; \backslash in\; R$, such that $T(a,b,x)=c\; \backslash ,$; and # $\backslash forall\; a,b,c,d\; \backslash in\; R,\; a\backslash neq\; c$, the equations $T(a,x,y)=b,T(c,x,y)=d\; \backslash ,$ have a unique solution $(x,y)\backslash in\; R^2$. When $R$ is finite, the third and fifth axioms are equivalent in the presence of the fourth. No other pair (0', 1') in $R^2$ can be found such that $T$ still satisfies the first two axioms. 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「Planar ternary ring」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.