A NOTE ON DIRECT-INJECTIVE MODULES

Abstract

In this paper, we study some more properties on direct-injective modules in the context of endoregular, SSP and SIP modules. We find the equivalent condition for a direct-injective module to be divisible. We also show that the endomorphism ring of an R-module M is a division ring if and only if M is a direct-injective module with (*) property. Finally, we study dc-rings and find their connections with hereditary rings and SSI-rings. © Palestine Polytechnic University-PPU 2019.