A generalization of supplemented modules

Abstract

Let R be an arbitrary with identity and I a right R-module. In this paper, we introduce a class of modules which is an analogous of delta-supplemented modules defined by Kosan. The module is called principally delta-supplemented, for all m E there exists a submodule A of M with M = mR + A and (mR) boolean AND A delta-small in A. We prove that sonic results of delta-supplemented modules can be extended to principally delta-supplemented modules for this general settings. We supply some examples showing that there are principally delta-supplemented modules but riot delta-supplemented. We also introduce principally delta-semiperfect modules as a generalization of a-semiperfect modules and investigate their properties.