iw-SPLIT MODULES

In this paper, the notions of iw-split modules and iw-split dimension are introduced, and some equivalent characterizations of these notions are given. With the help of iw-split modules and iw-split dimensions, new characterizations of DW rings, semi-simple rings, and Dedekind domains are given. More precisely, it is shown that R is a DW ring if and only if every iw-split module is an injective module; while R is a semi-simple ring if and only if every R-module is an iw-split module; and R is a Dedekind domain if and only if every factor module of an iw-split module is iw-split.