ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.47, no.5, pp.1539-1563, 2017 (SCI-Expanded)
Let R be an arbitrary ring with identity and M a right R-module. In this paper, we introduce a class of modules which is analogous to that of Goldie*-lifting and principally Goldie*-lifting modules. The module M is called principally G*-delta-lifting if, for any m is an element of M, there exists a direct summand N of M such that mR is beta(delta)*-equivalent to N. We also introduce a generalization of Goldie*-supplemented modules, namely, a module M is said to be principally G*-delta-supplemented if, for any m is an element of M, there exists a delta-supplement N in M such that mR is beta(delta)*-equivalent to N. We prove that some results of principally G*-lifting modules and Goldie*-lifting modules can be extended to principally G*-delta-lifting modules for this general setting. Several properties of these modules are given, and it is shown that the class of principally G*-delta-lifting modules lies between the classes of principally delta-lifting modules and principally G*-delta-supplemented modules.