关于BCI-代数和BCH-代数并代数的一些注记

Some Notes on the Unions of BCI-Algebras and BCH-Algebras

我们知道,BCK-代数有并代数的概念(见[1]),但一族BCK-代数的并代数的概念不可推广到BCI-代数(见[1]).1984年李欣曾定义了一个BCK-代数和一个BCI-代数的(LX)并代数。自然我们应当考虑一般性的问题:可否(用一种统一的方法)对任意两个BCI-代数定义其并代数?我们先作下列定义:

In this paper the authors discuss the question if there are the unions for any BCI-algebras or BCH-algebras. The authors point out: one can't define the unions for arbitrary BCI-algebras, but one can introduce the concept on ( LX ) union algebras; one also can't define the unions for arbitrary BCH-algebras, but one can introduce the concepts on the unions of non-negative BCH-algebras and ( GLX ) unions.