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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，通過引入相對co - ojective模的概念，我們給出了兩個提升模的直和仍是提升模的又一個充分條件，得到了一系列與擴張模相對偶的結(jié)論，作為提升模的推廣，在第三部分中引入了x -提升模的概念，討論了兩個x -提升模的直和仍是x -提升模的充分條件，作為推論可得到兩個提升模的直和仍是提升模的充分條件，在第四部分和第五部分中分別引入了fi -提升模， ssrs -模和弱提升模的概念，從三個不同方面推廣了提升模，并討論了這些模的基本性質(zhì)，如直和，直和因子等。