关于单BCI－代数的一些结果

SOME RESULTS ON SIMPLE BCI-ALGEBRAS

本文讨论了单ＢＣＩ－代数．证明了一个ＢＣＩ－代数是单的当且仅当它的子代数都是单的；给出了单ｐ－半单ＢＣＩ－代数的一种表示式；证明了一个ｐ－半单ＢＣＩ－代数是单的当且仅当它的阶是素数；这样得到了一批（无限多个）单ＢＣＩ－代数；证明了商ＢＣＫ－代数Ｘ／Ａ是单的当且仅当Ａ是Ｘ的极大理想．

In ths paper,we study the structure of simple BCI-atgebras. We show that a BCI-algebra is simple if and only if its subalgebras are all simple. We give an expression of the structure of simple p-semisimple BCI-algebras. We show that a p-semisimple BCI-algebra is simple if and only if its order is prime. Thus we obtain a lot of (infinite)simple BCI-algebras. We show that quotient BCK-algebra X/A is simple if and only if A is maximal ideal of X.