On Lifting Modules And Generalized Lifting Modules

In this paper, lifting modules are generalized and investigated. In section one, we list some conceptions and lemmas for later use. In section two, the sufficient condition that the direct sum of two lifting modules is lifting module is given, and we obtain a series of results that dual extending modules. 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.