ON ADS MODULES AND RINGS

Abstract

A right module M over a ring R is said to be ADS if for every decomposition M=S circle plus T and every complement T of S, we have M=S circle plus T. In this article, we study and provide several new characterizations of this new class of modules. We prove that M is semisimple if and only if every module in sigma[M] is ADS. SC and SI rings also characterized by the ADS notion. A ring R is right SC-ring if and only if every 2-generated singular R-module is ADS.