一类BCI-代数及其结构

A Kind of BCI-algebra and Its Structure

引入一类新的BCI-代数,并且讨论了它的基本性质,同时在BCK-代数与广义结合BCI-代数之间引入了星和概念,借此搞清了该类代数的结构.

In this paper, a new kind of BCI-algebra, i. e. generalized quasi-left-alternating BCI-algebra (GQLAB-algebra), is introuduced. A structure theorem of GQLAB-algebra is abtained as follows:Let 〈X; *, 0〉 is a GQLAB-algebra, then, (1) BCK-part B(X) of X is a quasi-alternating BCK-algebra; (2) BCK-complement L(X) of X is a generalized associative BCI-algebra; (3) X is the LX-union algebra of B(X) and L(X).