Abstract
We study the class of
ADS rings and modules introduced by Fuchs (1970)
[F]. We give some connections between this notion and classical notions such as injectivity and quasi-continuity. A simple ring
R such that
R
R
is ADS must be either right self-injective or indecomposable as a right
R-module. Under certain conditions we can construct a unique ADS hull up to isomorphism. We introduce the concept of completely ADS modules and characterize completely ADS semiperfect right modules as direct sum of semisimple and local modules.