TAIWANESE JOURNAL OF MATHEMATICS, vol.17, no.1, pp.239-257, 2013 (SCI-Expanded)
Let tau = (T,F) be a torsion theory. An R-module M is tau-lifting, if for any submodule N of M there exists a decomposition M = A circle plus B such that A <= N and N boolean AND B is tau-small in M. This definition unifies several definitions on generalizations of lifting property of modules. In the present paper, various results on tau-lifting modules are developed, many extending known results.