ET-Hollow Module and ET-Lifting Module

Abstract

Let M be a R-module;, where R be a commutative; ring with identity,

 In this paper, we defined  a new types of module namely “ET-hollow(ET-holl.) and ET-lifting(ET-lift.)  modules”. An R-module M is called ET-holl. module, if for all sub-module H of M then HM. An R-module M is called An R-module M is called ET-lifting  module, if for all H  M , there exists X M and LM, such that H=X+L. We give many characterizations of ET-holl. and ET-lifting  modules, Also we give the relation between T-hollow and ET-holl. and  relation between T-lifting  modules and ET-lift. modules.