W-supplemented modules

The purpose of this thesis is to investigate the properties of w-supplemented, totally w-supplemented and w-coatomic modules. A module M is w-supplemented module if and only if M is amply w-supplemented module. Although the class of w-supplemented modules is closed under extension with certain condition, the class of w-coatomic modules is closed under extension by short exact sequence. We give an example of a module M for which every submodule of w-supplemented module need not be w-supplemented. Every torsion module is (totally) w-supplemented over a Dedekind domain. If R is a semilocal ring, then every R-module is (totally) w-supplemented module. We prove that a module M is w-supplemented if and only if M is totally w-supplemented over a left V-ring. If M is a reduced and w-supplemented module, then M is w-coatomic.