R-Annihilator--Hollow Modules and R-Annihilator--lifting Modules

Abstract

Let be an unitary module on associative ring with identity. A sub moduleof an R-moduleis called-annihilator--small, if  for every c-singular submodule of an R-module,  implies that , where  In this paper, we introduce the concepts of -hollow modules and -lifting modules which are generalization -hollow modules and -lifting modules  with their properties.