Finite Lattices And Koszul Filtrations

Our paper is divided into three chapters.In the first chapter,we give an outline and some backgrounds of this paper.Also the motivation and the main results are explained and stated.In the second chapter,we give the definitions of some basic concepts which we need to understand our main results.In addition,some related known results are given and proved.Some of these results is not essential in proving our main results,we recall them for the following two reasons:firstly,they are the basic results in the field of Koszul algebra and are helpful to understand our main results and one will get some flavor of our research field by reading them,secondly,although our main results are not very simple and have been published in Communications in Algebra,they are rather short and so our paper has enough space for us to include these seemingly superfluous results.In the three chapter,we state and prove our main results.