ON U-TORSIONLESS MODULES AND U-NEAT MODULES

Abstract

Using U-torsionless module we characterize U-neat submodules and Au - injective modules. If M is a left R-module, U is E(M)-injective and Eu(M)/M does not contain a nonzero homomorphic image of a Utorsionfree module, then a submodule N of M is U-neat if and only if N = Eu(N)∩ M. Finally, we give the relationship between the Utorsionless modules and the Au-injective modules, and we also show the equivalent conditions of U-torsionless modules by inverse limit