基于一般的剩余格,引进了正则滤子的概念,给出了正则滤子的一些特征刻画,并且建立了正则滤子与其它一些特殊滤子(G-滤子、MV-滤子、Boolean滤子)之间的内在联系.证明了一个剩余格为正则剩余格当且仅当它的每个MP滤子是正则滤子.
In this paper,the concept of regular filters based on general residuated lattices is introduced,some characterizations of regular filters are derived,and the relations between regular filters and several other special filters(G-filters、MV-filters and Boolean filters) are established.Moreover,it is proved that a residuated lattice is regular if and only if its every MP filter is a regular filter.