Simple Dual Rickart Modules And Singular Simple Dual Rickart Modules

The concept of simple dual Rickart modules is introduced in Chapter 3.A module M is called simple dual Rickart if every simple image of M is a direct summand of M.Its basic properties are studied and it is proved that a ring R is a V-ring if and only if every right R-module is a simple dual Rickart module.The concept of singular simple dual Rickart modules is introduced and its properties are studied in Chapter 4.The relations between simple dual Rickart modules and singular simple dual Rickart modules are discussed,and GV-rings are characterized by singular simple dual Rickart modules.