关于伪BCI-代数的结合伪滤子与伪a-滤子（英文）

On Associative Pseudo-Filters and Pseudo-a Filters of Pseudo-BCI Algebras

给出伪BCI-代数中结合伪滤子及伪a-滤子的一些新性质,证明了以下重要结果:(1)伪BCI-代数的一个伪滤子是结合的当且仅当它是伪a-滤子;(2)一个伪BCI-代数是结合BCI-代数的充分必要条件是它的每一个伪滤子是结合的(或伪a-滤子);(3)伪BCI-代数的一个伪滤子是结合的(或是伪a-滤子)当且仅当它是群逆伪q-滤子,当且仅当它是群逆T-型伪滤子。

Some new properties of associative pseudo-filters and pseudo-a filter of pseudo-BCI algebras are presented. The following important results are proved： （1）a pseudo-BCI filter of a pseudo-BCI algebra is associative if and only if it is a pseudo-a filter; （2）a pseudo-BCI algebra is an associative BCI-algehra if and only if its every pseudo-BCI filter is associative （or pseudo-a filter）; （3）a pseudo-BCI filter of a pseudo-BCI algebra is associative （or pseudo-a filter ） if and only if it is an anti-grouped and pseudo-q filter, if and only if it is anti-grouped and T-type pseudo-BCI filter.