Mittag-Leffler条件刻画了一类特殊的逆向系统，该条件已经被成功的用于解决同调代数中的许多公开问题。在本项目中，我们将研究Mittag-Leffler条件和余挠对之间的关系，探讨严格的Mittag-Leffler条件的判别方法，寻求严格的Mittag-Leffler条件和一些同调维数之间的联系，将一些重要的同调不变量转化为一定的Mittag-Leffler条件，借助Mittag-Leffler条件及其同调理论对两个公开问题展开研究：1.是否所有的Gorenstein投射模都是Gorenstein平坦的；2. Gorenstein内射盖存在的一般条件是什么，探索解决这两个问题的新思路和新方法。

Mittag-Leffler conditions are defined by special inverse systems, Such conditions have been successfully employed in a number of different problems in homoogical algebra. In this project, we will study the relations between Mittag-Leffler conditions and cotorsion pairs, and the estimation method of strict Mittag-Leffler conditions, we will translate some important homological invariants into certain Mittag-Leffler conditions, and explore the connections between Mittag-Leffler conditions and some homological dimensions. Employing the Mittag-Leffler condition and its homological theory, we will focus on two well known open problems in Gorenstein homological algebra: 1.Whether all Gorenstein projective modules are Gorenstein flat or not; 2.The problem of the existence of Gorenstein injective cover. We want to look for effective methods of solving the two problems .