Fδ-Supplemented Modules

Abstract

In this article, we define a (an amply) F-delta-supplemented module in category of R-Mod. The general properties of F-delta- supplemented modules are briefly discussed. Then, concentrating on the F-delta-small submodule, we find the necessary and sufficient condition for F-delta- supplemented modules. Also, we introduce ascending chain condition for F-delta-small submodules of any module and establish a basic theorem for amply F-delta-supplemented modules by using pi-projectivity.