On cofinitely Rad-supplemented modules

Abstract

Let R be a ring and M be a left R-module. In this work some properties of (amply) cofinitely Rad-supplemented modules are developed. It is shown that if M contains a nonzero semi-hollow submodule then M is cofinitely Rad-supplemented if and only if M/N is cofinitely Rad-supplemented. Morever a module M with small radical is cofinitely Rad-supplemented such that Rad-supplements are supplements in M, then M is cofinitely supplemented. In addition, a ring R is left Rad-supplemented if and only if every left R-module is amply cofinitely Rad-supplemented. Also, we give a characterization of generalized semiperfect modules. © 2009 Academic Publications.