关于BCI-代数的超幂零根与特殊根

ON THE SUPERNILPOTENT RADICALS AND SPECIAL RADICALS FOR BCI-ALGEBRAS

本文利用肖祖文在[4]中提出的BCI-代数的理想子代数的概念,给定了弱单BCI-代数与弱素BCI-代数的概念,同时还引入了有心BCI-代数的概念.然后具体地讨论了有心BCI-代数类及其所确定的上根BCI-代数类.最后建立了超幂零根BCI-代数类与特殊BCI-代数类.同时,我们还给定与证明了一个BCI-代数的特殊根的一个刻划.

In this paper, by using the concept of ideal subalgebras in BCI-algebra given by Xiao Zuwen in[4], we give the concepts of weak simple BCI-algebra and weak prime BCI-algebra. At the same time, we introduced the notion of BCI-algebra with heart. Then,we concretely discussed the class of all BCI-algebra with heart and it determines the upper radical. Finally, we establish the notions of supernilpotent radicals and special radicals in BCI-algebras. At the same time, we give and prove a characterization of special radical of a BCI-algebra.