Research On Two Classes Of Idempotent Residuated Lattices

In the study of residuated lattice theory,idempotent residuated lattice is an important research field.In this paper,we study the properties and structures of two classes of residuated lattices using the Green-D relation of semigroups and the natural partial order relation.The main work of this thesis is as follows:In chapter 1,we introduce the research history and background of residuated lattices,as well as the current research status of idempotent residuated lattices,and provide relevant preliminary knowledge.In chapter 2,we study the properties of idempotent residuated chains and then obtain a new constructing method of idempotent residuated chains,and provide a structure theorem for this class of residuated lattices.In chapter 3,we extend the research work in the previous chapter by studying the properties of conic idempotent residuated lattices,and obtain a structure theorem for such class of residuated lattices and then apply the obtained results to conic idempotent commutative residuated lattices.In chapter 4,we summarize all the research results of this thesis,and provide future work ideas for further study contents.