A Principally Radg-Lifting Modules

In this article we present a new class of modules which is named as a principally -lifting modules. This class termed by Principally -lifting in this work which defined as, a module  is called Principally -lifting if for every cyclic submodule  of  with , there is a decomposition  such that  and  is g-small in . Thus, a ring  is called Principally -lifting if it is a principally -lifting as -module. We determined it is structure. Several characterizations, properties, and instances are described of these modules'.