Local lifting Modules with Some of Their Generalizations

Abstract

To consider R is a commutative ring with unity, M be a nonzero unitary left R-module,Mis known lifting moduleif for every submodule N of M there exists a submodule A of N such that M = A .Local lifting moduleis a strong form of lifting module, where an R-module M is knownlocal lifting moduleif M has a unique maximal submodule N and each submodule of N there exists a submodule A of N such that M = A  and N B is small submodule of B.The current study deals with this class of module and give several fundamental properties related with this concept.