On Ads-Modules With the Sip

Abstract

The class of ads modules with the SIP (briefly, SA-modules) is studied. Various conditions for a module to be SA-module are given. It is proved that for a quasi-continuous module M, M is a UC-module if and only if M is an SA-module. Also, it is proved that the direct sum of two SA-modules as R-modules is an SA-module when R is the sum of the annihilators of these modules.