FI代数中MP滤子的等价刻画

Characterizations of MP-filters of (regular) FI-algebra

Fuzzy蕴涵代数(简称FI代数)是逻辑蕴涵连接词的代数化,揭示了蕴涵算子所具有的共同特征.为探讨FI代数中MP滤子与正规MP滤子的性质,给出了FI代数中非空子集成为MP滤子的充要条件.通过反例说明了在FI代数中MP滤子不必是正规MP滤子.指出在正则FI代数中正规MP滤子一定是MP滤子.还利用正则FI代数中的MP滤子和正规MP滤子对可交换FI代数做出了等价刻画.

Fuzzy implicative algebras （in short, FI-algebras）, is a kind of algebraic abstractions of implicative connections. FI-algebras reveals the common characters of implication operators. In this paper, to discuss further properties of MP-filters and normal MP-filters of FI-algebras, a necessary and sufficient condition for hot, empty set to be MP-filters in FI-algebras is given, and counterexamples reveal that MP-filters are not necessarily normal MP-filters. In regular FI-algebra, it is proved that normal MP-filters are all MP-filters. Characterizations for exchangeable FI-algebras are also obtained.