As the generalization of lifting modules , in section three , the conception of x - lifting module are defined and we study the sufficient condition for the direct sum of two x - lifting modules is x - lifting module . as the corollary , the sufficient condition that the direct sum of two lifting modules is lifting module is obtained . in section four and five , the conceptions of fi - lifting modules , ssrs - modules and weak lifting modules are introduced , which also generalized the lifting modules , and we study their basic properties such as direct sum , direct summand etc 在第二部分中，通过引入相对co - ojective模的概念，我们给出了两个提升模的直和仍是提升模的又一个充分条件，得到了一系列与扩张模相对偶的结论，作为提升模的推广，在第三部分中引入了x -提升模的概念，讨论了两个x -提升模的直和仍是x -提升模的充分条件，作为推论可得到两个提升模的直和仍是提升模的充分条件，在第四部分和第五部分中分别引入了fi -提升模， ssrs -模和弱提升模的概念，从三个不同方面推广了提升模，并讨论了这些模的基本性质，如直和，直和因子等。
