剩余格中的素(p)滤子

Prime(P)Filters of Residual Lattices

在剩余格中定义了一类特殊的素(p)滤子,讨论了它们的结构和性质.证明了该剩余格中的蕴涵运算可由这些特殊的素(p)滤子所确定,并且这些特殊的素(p)滤子的全体构成一个剩余格,它与原剩余格具有格蕴涵同构关系.当剩余格是MTL代数、IMTL代数、BL代数、MV代数或R0代数时,上述结论也成立.

A special kind of prime（p） filters are defined in a residual lattice,then their structures and properties are discussed.It is proved that the implication operation in the residual lattice is determined by these prime（p） filters,and all of these prime（p） filters compose a residual lattice,which is lattice implication isomorphic to the former residual lattice.The conclusion is suit for MTI. algebra,IMTL al gebra,BL algebra,MV algebra and R0 algebra.