A ring is called a reduced ring if it has no nonzero nilpotent elements. In this thesise we continue the study of nonsingular, armendariz, ps-Armendariz, ZI and reduced modules and rings show that reduced modules are symmetric and symmetric modules are ZI and show that flats modules over reduced rings are reduced. Also flat modules over symmetric rings are symmetric. Similary show that reduced modules are ps-Armendariz and ps-Armendariz modules are ZI. Next characterize rings over which all modules are reduced (symmetric). Also, introduce the concepts of regular and strongly regular rings, V-rings and p-V-rings and study its some properties and extend these results to modules and show that regular ZI rings are strongly regular and therefore reduced, left and right V-ring. We study the relationships of reduced modules with semiprime (semiprimitive) modules and other related
