关于BCI－代数根的补根与对偶根

Supplementary and Dual Radicals in BCI-Algebras

本文首先给定了ＢＣＩ－代数根的补根与对偶根的概念，并证明了遗传根的补根的存在性，其次得到了ＢＣＩ－代数中ｐ－根的补根的一个具体刻划，同时证明了ｐ－根是一个对偶根。最后证明了每一个根性质都存在一个补根，且根Ｒ的补根是由所有非Ｒ－半单的亚直既约ＢＣＩ－代数确定的上根。

in this paper. we first give the concepts of supplementary radical of a radical property and the dual radical in BCI-algebras. And we have proved that the existence of the supplenientary radical of a hereditary radical. Then we obtain also a concrete characterization of the supplementary radical of p-radical. At the same time, we have proved that the pradical is a dual radical. Finally we have proved that the existence of the supplementary radical for every radical, and the supplementary radical of the radical R is the upper radical determined by all non R-semisimple subdirectly irreducible BCI-algebras.