单纯BCI-代数的结构

ON STRUCTURES OF SIMPLE BCI-ALGEBRAS

本文建立了周期BCK-代数的概念,从而把姜豪^([1])的有限单BCK-代数结构定理推广到无限的情形,而且我们的证明本身也简化了文[1]中有限单BCK-代数结构定理的原证,此外,我们还建立了单纯真BCI-代数的一个结构定理,因而完整地解决了单纯BCI-代数的结构问题。

In this paper we have introduced the notion of the cycle BCK-algebras, extended the structure theorem of finite simple BCK-algebras by Jiang Hao^([1])to the case of infinite simple BCK-algebras, and our proof itself has simplified the original proof of the structure theorem in [1]. Moreover, we have established the structure theorem for simple proper BCI-algebras. Therefor the problem of the structures for simple BCI-algebras has totally been solved.