可分支BCI-代数

Separable Branches BcI-algebras

本文将引入可分支BCK—代数及可分支BCI—代数,证明了原子生成的BCK—代数是可分支BCK—代数以及其一个充要条件,从而获得了在可分支BCK—代数中,交换BCK—代数是原子生成的BCK—代数;在原子生成的BCK—代数中,正关联BCK—代数是交换BCK—代数,从而是关联的,并且得到可分支BCK—代数是由原子及不降元生成的BCK—代数;可分支BCI—代数是由原子、不降元及极小元生成的BCI—代数。

Ie this paper, the author introduces separable branches BCK-algebras and separable branches BCI-algebras. and thus obtains a sufficient and prerequisite of BCK-algebras generated by atoms; separable branches BCK-algebras generated by atoms and non-depressed elements; separable branches BCI-algebras generated by atoms and non-depressed elements and minimal elements; and some property on separable branches BCK-algebras. And in particular, the author deals with the Finite BCK-algebras generated by atoms and nondepressed elements; and Finite BCI-algebras generated by atoms and non-depressed elements and minimal elements.