【摘要】 证明了FBZ-代数按所规定的偏序 ,确实是一偏序集 ,即若X是FBZ-代数 ,则 x∈X ,x≤x.讨论了FBZ-代数与BCI_代数的关系 .证明了满足条件x (yz) =y (xz)的FBZ_代数 ,如果令 X =X ,x y=yx ,0 =1,则 ( X , ,0 )一定是BCI-代数 ;反过来 ,若 (X , ,0 )是BCI-代数 ,令 X =X ,xy =y x ,1=0 ,则 ( X , ,1)是FBZ-代数 .还引入了正则FBZ -代数的概念 ,给出了正则FBZ-代数的一个特性 .更多还原

【Abstract】 This essay proves that FBZ-algebra is a partial-ordering group aecording to the set partial-ordering. That is, if X is the FBZ-algebra, then x∈X,x≤x. In addition, the essay studies the relationship between FBZ and BCI-algebras. And FBZ-algebra is proved under the full cordition x(yz)=y(xz), if =X, x*y=yx,0=1, then(,*,0)must the BCI-algebra; otherwise, if (X,*,0)is BCI-algebra, and =X, xy=y*x, 1=0, the(,,1) is FBZ-algebra. At the end of the essay, the conception of FBZ-algebra of regularity is introduced and a characteristic of it is provided.更多还原