Direct sum of various generalizations of h-lifting modules.

In this work, h w -lifting modules, a special extension of h -lifting which is a further generalization of lifting modules, are studied. Here, we observed that finite direct sum of h w -lifting modules may not be h w -lifting, so we provided various sufficient conditions for which h w -lifting modules are closed under direct sum. Moreover, we have introduced and studied the properties of a new version of h -lifting module namely, m h -lifting, m h w -lifting and completely m h -lifting modules and develop some more properties of the h w -lifting modules in terms of these modules. Further, we proved that if the direct sum of arbitrary family of hollow modules is m h -lifting, then the arbitrary direct sum of m h -lifting R -module is again m h -lifting. [ABSTRACT FROM AUTHOR]